Question

Solve 15^2x = 36. Round to the nearest ten-thousandth.

Answer 1

@whpalmer4

Answer 2

A. 0.6616
B. 2.6466
C. 1.7509
D. 1.9091

Answer 3

Is that \[15^{2x} = 36\]?

Answer 4

Yes, it must be, because I get one of those answers :-)

Do you remember the property of logs that says \[\log (x^a) = a\log(x)\]? You can use that to solve this problem by taking the log of both sides and using that property.

Answer 5

That means
\[2x \log 15 = \log 36\]Now just solve for \(x\) and put the calculator to work

Answer 6

Yes

Answer 7

x=270 ?

Answer 8

Ik it's wrong please let me explain ...

Answer 9

was I supposed to do 36*15 ?

Answer 10

\[2x \log 15 = \log 36\]Divide both sides by \(\log 15\) to get\[2x = \frac{\log 36}{\log 15}\]Can you do the rest? The answer had better be less than 1, because if \(x =1\), then \(15^{2x} = 15^2 = 225\) which is much bigger than 36!

Answer 11

I got 1.323283792

Answer 12

in fact, you could work it out in your head close enough to get the right answer!

hmm. that's 2x the right answer...did you remember to divide by that 2 in front of \(x\)?

Answer 13

A. 0.6616

Answer 14

Thanks again

Answer 15

one more please i promise and i will leave you alone ?

Answer 16

So, you could estimate this as follows:

\[15^{2x} = 36\]\[15^x*15^x = 36\]\[15^x = \sqrt{36}\]\[15^x = 6\]\[15^{1/2} = \sqrt{15} \approx \sqrt{16} = 4\]so it has to be bigger than 1/2 and smaller than 1. You could try 2/3:
\[15^{2/3} = \sqrt[3]{15^2}\]and because \[15^2 = 225\] and \[6^3 = 216\]that means that \[15^{2/3}\approx 6\]and the guess of \(x = 2/3\) is pretty close!

Answer 17

or, if you're like me, and memorized a handful of logarithms:

\[15^{2x} = 36\]\[x = \frac{\log 36}{2\log 15}\]but \[36=6^2 = 2^2*3^2\]so \[\log 36 = 2\log 2+2\log3 = 2*0.30103 + 2*0.477121 \approx 1.5563\]and \[\log 15 = \log(3*5) = \log3 + \log 5 \approx 0.477121 + 0.69897 \approx 1.17609\]so our answer is \[x = \frac{1.5563}{2*1.17609} \approx 0.661642\]just like you got, except without a calculator (except to do the division)

Answer 18

what's the other problem?