5

Write as a single logarithm_ 2 log1x + 2 1 log1oy 3 log1oz 3 logoa Enter a, b, C, d, or e_ + Vy a_ log10 93 x2a3 b_ log10 2 X2 C. log10- Vy 2333 x2 d. log10 - 5 2 X...

Question

Write as a single logarithm_ 2 log1x + 2 1 log1oy 3 log1oz 3 logoa Enter a, b, C, d, or e_ + Vy a_ log10 93 x2a3 b_ log10 2 X2 C. log10- Vy 2333 x2 d. log10 - 5 2 X e log10 4 a3 23

Write as a single logarithm_ 2 log1x + 2 1 log1oy 3 log1oz 3 logoa Enter a, b, C, d, or e_ + Vy a_ log10 93 x2a3 b_ log10 2 X2 C. log10- Vy 2333 x2 d. log10 - 5 2 X e log10 4 a3 23



Answers

Express each as the logarithm of a single quantity.
$$\frac{1}{2} \log _{b} a-2 \log _{b} 5-3 \log _{b} x$$

The given question is I do log tapes this be upon today plus Thio love. Why this b form for my nest? Oh, fine Flaw deep this be no drinking that in the contribution form we have too buttery long necks This be bless to you before No Why this b minus five I love you. Best be. It is equal Do law off It's to the power off by three b Bless off Why did the poverty by four this be minus No jet to the bar Fire Best being in continuation We have no best big X to the power to buy three Why did the party by four minus law judge it apart? Five best being which is equal Do not this be Thanks A squad This one and do four. Why you? My name is low. I did but five Best be that is equal. Do longest be this it counts Thinks it's squad and food like you. And then Do you bought five? This is the fun Vee jumped on. This is the answer

Consider the given expression using the powerful Michelle. Right? This is law based be all expert one by two less young based being off wipe over two by three. Now using the product, you'll let us combine these expressions so we get long based B o exp over one way to wipe over two by three.

Consider the human expression. So using the power rule, we get law based be off export one by two Minus law based Bigelow Wipe over to wait three. Now let us combine these two dumps using the potion. True. So we get no base. Be off. Explore one by do it by white over two by three.

All right, We have this expression that we want to combine into a single longer of them, and I'm going to start doing something that maybe you wouldn't expect. I'm going to rearrange the terms a little bit and put the third lager them first because I like to start with a positive lager of them and go from there. Okay. Now notice that there's a constant in front of each lager of them. If you look, maybe one of these should be a Z. I think I need to change that to a Z. There. There we go. Okay. Notice there's a constant in front of each lager them. We have a 1/2. We have a three. We have a two. And according to the power rule, those could be brought up and be made into exponents. So we have log base B of Z to the 1/2 minus log base B of X cubed minus log base B of y squared. Okay. Now, if you're subtracting a lager them from another, you can use the quotient rule and combine that into the log of a quotient. And because we're subtracting two logarithms, we're going to have two factors and the denominator of that quotient. So that's going to give us log base B of Z to the 1/2 divided by X cubed times y squared. So whichever ones you subtract those go on the bottom and then finally, if you don't want to leave it as you to the 1/2 you could change that 1/2 power to a radical square root, and you would have log base B of square woozy over X cubed Why squared?


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