# Solve the equation by using logarithms

The equation is

$64(12)^{8x} = 195$

the steps I have done so far.

• $12^{8x} = 195/64$
• $8x \cdot \ln(12) = \ln(195/64)$
• $8x = (\ln(195/64))/(\ln(12))$

not sure how to divide $8x$ to get $x$ by itself for the final answer with the ln's

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Wait a minute --- you've done all the log stuff, now you're down to $8x=A$, and you can't solve that for $x$? – Gerry Myerson Dec 4 '12 at 23:36
@GerryMyerson that is correct. I took a break from math for about 8 months and I know you divide 8 on both sides, but the ln's are confusing me. – Tyler Zika Dec 4 '12 at 23:37
Don't let them confuse you! Dividing by $8$ is dividing by $8$, no matter what the other side of the equation looks like. What would you do if it were $8x=93/42$? – Gerry Myerson Dec 4 '12 at 23:38
@GerryMyerson x = 8(93/42)? – Tyler Zika Dec 4 '12 at 23:40
@GerryMyerson oh its x = 93/336 – Tyler Zika Dec 4 '12 at 23:43

when you divide $8x = (\ln(195/64))/\ln(12)$ you get $x = (\ln(195/64))/(\ln(12)(8))$. The 8 only affects the bottom denominator of equation when you divide a fraction. thank you @GerryMyerson
It's better to write $x=\frac{\ln(195/64)}{8\ln(12)}$ using the code $x=\frac{\ln(195/64)}{8\ln(12)}$. See MathJax basic tutorial and quick reference. – Américo Tavares Dec 5 '12 at 0:15