Can someone help me with this logrithims question?
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Question

asnaseer · Answer

do you know how to do these problems yourself or are you just looking for the answers?

anonymous · Answer

I think wolfram alpha gave me like 3 square root(3) times 10 to the power of like 3/4 or 4/3..but it said it was wrong. My tutor didnt know how to do it at all

anonymous · Answer

Yeah, I know how to do these problems. In fact, I had a tutor yesterday. Its just that the problems online for this chapter are very different than the ones in the book

asnaseer · Answer

ok, I will try and show you how to do this step-by-step, and then hopefully you should be able to tackle other questions like this yourself.

anonymous · Answer

okay, I did most of them. I only have about 7 online, 2 of them, I cant do. This one and the other one we were just on. I have not looked at the other ones

asnaseer · Answer

$$\frac{log(x^3)+log(x^4)}{log(90x)}=\frac{3log(x)+4log(x)}{log(90)+log(x)}=\frac{7log(x)}{log(90)+log(x)}$$so we get:$$\frac{7log(x)}{log(90)+log(x)}=3$$multiply both sides by the denominator of the left-hand-side:$$7log(x)=3log(90)+3log(x)$$$$4log(x)=3log(90)$$$$log(x^4)=log(90^3)$$$$x^4=90^3$$$$x=\sqrt[4]{90^3}$$this can be simplified further - do you understand so far?

asnaseer · Answer

I need to go now, hopefully you can finish this off. leave a comment here if you get stuck and I'll try and help again when I am back online tomorrow.

anonymous · Answer

Hmm the way my tutor and I started it, we combined log(x^(3) and log (x^(4) into one. so it became log (x^(7)). By the way, Your answer is right! Thank you very much!