Question

Isolate x from:

Answer 1

take log

Answer 2

\[(\log_{7}9)/ (3\log_{7}4-1) \]

Answer 3

\[18\times 7^x = 8\times 4^{3 x-1}\]

Answer 4

no gimmicks here you just have to grind it out. maybe divide by 2 first but after that it is take the log and use algebra

Answer 5

\[9\times 7^x=4\times 4^{3x-1}=4^{3x}\]
\[\ln(9)+x\ln(7)=3x\ln(4)\]

Answer 6

I end up with x=(log(256))/(long9-log5)

Answer 7

\[\ln(9)=x(3\ln(4)-\ln(7))\]
\[x=\frac{\ln(9)}{(3\ln(4)-\ln(7))}\]

Answer 8

Take the log of both sides:
\[\log(18*7^x)=\log(8*4^{3x-1}) \rightarrow \log(18)+\log(7^x)=\log(8)+\log(4^{3x-1})\]
\[\log(18)+x \log(7)=\log(8)+(3x-1)\log(4) \rightarrow \log(18)-\log(8)=(3x-1)\log(4)-x \log(7)\]
\[\log(18)-\log(8)=(3x)\log(4)-x \log(7)-\log(4)\]
\[\log(18)-\log(8)+\log(4)=x(3 \log(4)-\log(7))\]
\[x=\frac{\log(\frac{4*18}{8})}{\log(\frac{4^3}{7})}\]
I hope my algebra is right.

Answer 9

I have the same as you satellite, I just combined the bottom log.

Answer 10

lots of ways to write the answer, but i think dividing by two and then rewriting the right hand side as
\[4^{3x}\] makes life easier

Answer 11

malevolence has same answer i think. more algebra though!

Answer 12

One last question, why did you choose Natural logarithm. Can I choose Log in base 10?

Answer 13

I log base 10. You could do log base pi if you wanted. As long as you do the operation to both sides, the base is arbitrary.

Answer 14

I did log base 10***

Answer 15

oh right!
\[\frac{4\times 18}{8}=9\]!

Answer 16

you can choose any base you like. but for practical purposes if you want a decimal out of this you have to choose a log on your calculator, so base ten or base e will do

Answer 17

yeah, even base pi!

Answer 18

shy dont choose log base 2 then. I think it simplifies more. log2(2^(6x)) =6x, right?