5

Suppose that f(c)dz =4f(c)dr = 0,g(r)dx ~3 ["~9)dzThen,6" (fke) g(c) )dr 10...

Question

Suppose that f(c)dz =4f(c)dr = 0,g(r)dx ~3 ["~9)dzThen,6" (fke) g(c) )dr 10

Suppose that f(c)dz =4 f(c)dr = 0, g(r)dx ~3 ["~9)dz Then, 6" (fke) g(c) )dr 10



Answers

Given that 1og10 2 = 0.3010 and 1og 10 3 = 0.477 1,find each logarithm without using a calculator. $$ \log _{10} 6 $$

Okay so we're gonna be getting this log rhythm into log base 10 of three and twos and then using the known values to find the actual value of this log rhythm. So the first thing we're gonna do is split it up into log base 10 of the numerator minus log base 10 of the denominator. Using the properties of logarithms. And then the next thing we want to recognize is that nine is three squared and four is two squared. So we're gonna rewrite this as log base 10 of three squared minus log base 10 of two squared. And now we can use the properties of logarithms that says whenever we have the log of some number races some exponents we can actually bring that exponents out in the front of the log rhythm. Okay so we're gonna have this is equal to two times log base 10 3 -2 times log base 10 of two. And so now we can go ahead and plug in. What log base 10 of three and log base 10 of two are equal to. So that's gonna be two times 20.477 minus two times 20.3 one. And so um I mean just plug And since my calculator we have two times point 477 minus two times .30. 1. Which is equal to .352

So we're gonna be using these two known values log base 10 of two and log base 10 of three. To figure out the value of log base 10 of 12. And so the way that we can do this is by noticing that log base 10 of 12 is equal to log base 10 of three times two times two. And then the next thing we want to do is just use the properties of logarithms that tell us when we have the log of multiple numbers being multiplied together, it's equal to the log of the first number, plus the log of the second number plus the log of the third number and so on. Depending on how many numbers you have multiplied together. Here we have three, so we're gonna have three logs And now we can go ahead and plug in. Um what each of these values are, so we have .477 plus .301 plus point 301. So 301 plus three or one is 602. So this is 6020.477 plus 0.6 of two, Which is equal to 9 7. So 1.079

Okay. So we're gonna be getting this log rhythm into a form of log based tens of two and three and then using the known values that were given to actually solve and figure out the value of this log rhythm. And so the first property that we're gonna be using is whenever we have the log of one number divided by another sequel to the log of that first number or the numerator minus the log of the second number. And so now that we have it in this form we already have a log base 10 of two. So now we just need to get rid of this log base 10 of nine and replace it with only log based 10 of threes. And so the way we can do that is by noticing that nine is three squared. And then using the properties of logs to take that too and bring it out front of the log rhythms. We're gonna have log base 10 of two minus two times log base 10 of three. And now we can go ahead and plug in the values for log base 10 of two and three. So log base 10 of two is point oh three You're sorry .301. And then log base 10 of three was .477. And so I'm just gonna plug this into my calculator. We have two times point 477 and then we have point to .301- that value. And that is equal to negatives 0.6- .653

Okay, so let's evaluate this without a calculator. So this is Greater than log 10 of 16/27. But smaller than book tail off 27/27. Okay, so this equals to log 10 of 16 minus log 10 of 27. Okay? Or you can write this as log 10 of 2 to the 4th- Log 10 of 3 to the three. Okay. So this goes to four times log 10 of 2 -3 times long. Three o'clock. 10 of three. Okay, so this equals the four times 0.3010 minus. Okay, so we have these days point point 20 40 minus one point for 1.4313. Okay, so this is around minus the real point two To service three. Okay. And Lock 10 off. Mhm. 27 hours seven. It goes to a lot 10 of one. It goes to zero. Okay. Yeah. So log hey off 20/27 Is greater than -0.2273. But smaller than zero


Similar Solved Questions

5 answers
SupposeR'/x andintegersDecidesuhspuce of ? 1
Suppose R'/x and integers Decide suhspuce of ? 1...
4 answers
Of 30 random selcted I)) Bosed on sask 9o % canfsdence intec Va| Ahnuis ( 'ar fcnfali in 0 nQ_ crtx js fvem 47. to 50.2 inches Find Hw nvz'^ of €rfo 2) A <nf,dnk nterval fot Peo lt;o~ h,S mo / of erf of cf 075 Txtermink the 4xt4 4h confidenc inkrval
of 30 random selcted I)) Bosed on sask 9o % canfsdence intec Va| Ahnuis ( 'ar fcnfali in 0 nQ_ crtx js fvem 47. to 50.2 inches Find Hw nvz'^ of €rfo 2) A <nf,dnk nterval fot Peo lt;o~ h,S mo / of erf of cf 075 Txtermink the 4xt4 4h confidenc inkrval...
1 answers
Sketch the indicated set. Describe the boundary of the set. Finally, state whether the set is open, closed, or neither. $\{(x, y): 2 \leq x \leq 4,1 \leq y \leq 5\}$
Sketch the indicated set. Describe the boundary of the set. Finally, state whether the set is open, closed, or neither. $\{(x, y): 2 \leq x \leq 4,1 \leq y \leq 5\}$...
5 answers
Suppose $N=15$ and $r=4$. What is the probability of $x=3$ for $n=10 ?$
Suppose $N=15$ and $r=4$. What is the probability of $x=3$ for $n=10 ?$...
5 answers
Caklum Ierch rinicctcd Jsmill smount ot rsdia Klic Gkriumn into an indakdusl: bboodstresm The cakium tCnJ rng in thc Motaitrcxn (nmilligrs pr cubk centimctcr) ( dare alter Lc Lutbl inkcction isahenbythoceujton C() 1(2+1)Relethesmulton thcklE'duealtcu ltutulinkcctothc Arnourtol rJdojctivaclkeilno Lhouit Qulltnet Httnarted InetOU_ Caeneon Rdji halnn Iyour angwerconectio?Findtne tatc ot change otcakriumImneaIntntin_datcnpierou;
Caklum Ierch rinicctcd Jsmill smount ot rsdia Klic Gkriumn into an indakdusl: bboodstresm The cakium tCnJ rng in thc Motaitrcxn (nmilligrs pr cubk centimctcr) ( dare alter Lc Lutbl inkcction isahenbythoceujton C() 1(2+1) Rele thesmulton thcklE 'duealtcu ltutulinkcctothc Arnourtol rJdojctivaclke...
5 answers
2 8 H 2 X 1 } L H L 22 1 Ju 628 2 J 0 [ 1 1 1 #1 1 1 j 2 J W 0 1 1 5 1 0 1 L 1
2 8 H 2 X 1 } L H L 22 1 Ju 628 2 J 0 [ 1 1 1 # 1 1 1 j 2 J W 0 1 1 5 1 0 1 L 1...
5 answers
The area of the interval liesbetween =z2.11 and =z2.47 is .
The area of the interval lies between =z2.11 and =z2.47 is ....
5 answers
Fill in the intermediates and propose suitable reagents for the following transformationsOCH3 HzotOHHzo1. SOCl2 2. CH3OHOHHaNNzH4CgH1oKCN; HzoOH OH
Fill in the intermediates and propose suitable reagents for the following transformations OCH3 Hzot OH Hzo 1. SOCl2 2. CH3OH OH HaN NzH4 CgH1o KCN; Hzo OH OH...
5 answers
Question 10ptsUpon hydrogenation to produce cyclohexane, which compound would be expected to release the most energy?Question 113 ptsUpon hydrogenation to produce cyclohexane. which compound would be expected to release the least energy?
Question 10 pts Upon hydrogenation to produce cyclohexane, which compound would be expected to release the most energy? Question 11 3 pts Upon hydrogenation to produce cyclohexane. which compound would be expected to release the least energy?...
5 answers
0 Il H_CH-~C COOH (CH2)2 8 CHa
0 Il H_C H-~C COOH (CH2)2 8 CHa...
5 answers
With random sample of size n-121. Someone (X proposes 0.12s,X + 0.12s) to be confidence interval for p , then the Jevel confidence interval [OI / :3,0081%957Uocaot6"MDC
With random sample of size n-121. Someone (X proposes 0.12s,X + 0.12s) to be confidence interval for p , then the Jevel confidence interval [OI / : 3,00 81% 957 Uocaot 6" MDC...
5 answers
3. Find the area of the region bounded by the graph of y cos(1) and the I-axis between I =t/20 andUse the graph below to find the value of f(z) dr.v = f(r)2
3. Find the area of the region bounded by the graph of y cos(1) and the I-axis between I =t/2 0 and Use the graph below to find the value of f(z) dr. v = f(r) 2...
5 answers
Find the limit or indicate that it does not existlim sin - '&)i - (cos3J + ( tan7)*]Select the correct choice below and, if necessary; fill in the answer box in your choiceOA lim sin Z)i+1 cos HJ - ( tn3)*]-Oi-O-€k 6I (Type an exact answer; using I and radicals as needed
Find the limit or indicate that it does not exist lim sin - '&)i - (cos3J + ( tan7)*] Select the correct choice below and, if necessary; fill in the answer box in your choice OA lim sin Z)i+1 cos HJ - ( tn3)*]-Oi-O-€k 6I (Type an exact answer; using I and radicals as needed...

-- 0.020571--