Question

10^x+3 = 6^2x solve for x

Answer 1

is it like this?
\[10^{x+3} = 6^{2x}\]

Answer 2

start with
\[(x+3)\ln(10)=2x\ln(6)\] and solve for x

Answer 3

assuming joemath is right

Answer 4

yeah thats how it is

Answer 5

change the ln to log, it will make things a smidge easier because:
\[\log(10) = 1\]

Answer 6

I got that far but I don't understand how to work with the logs when one is log of 10 and the other is log of 6

Answer 7

its something you would need a calculator for to figure out exactly what the answer is. Just leaving it as "log(6)" might be better.

Answer 8

\[(x+3) = 2xlog(6) \Rightarrow x-2xlog(6) = -3 \Rightarrow x(1-2\log(6))=-3\]
\[\Rightarrow x = \frac{-3}{1-2\log(6)}\]

Answer 9

oh okay i just did it out and I see what I did wrong. Thanks so much! (: