Problem involving change of base of Logarithm

[chijioke]

I must be missing something. You want to get the logs to the same base. Great, good thinking. Do it first. But once you have [imath]\log_5(5)[/imath], that reduces to 1. Why mess around when that obvious simplification is staring you in the face?

[math] 9 \log_x (5) = \log_5(x) \implies 9 * \dfrac{\log_5(5)}{\log_5 (x)} = log_5(x) \implies \dfrac{9}{\log_5(x)} = \log_5 (x) \implies \\ 9 = \{\log_5(x)\}^2 > 0. [/math]
Now you could do a u-substitution, but you could directly take the square roots of both sides of the equation. Then what?

To chijoke. you are hard-headed are you not?
[imath]9\log_x(5)=\log_5(x)\\9\dfrac{\log(5)}{\log(x)}=\dfrac{\log(x)}{\log(5)}\\9\left[\log(5)\right]^2=\left[\log(x)\right]^2\\ 3\log(5)=\log(x)\text{using the square root}\\x=125 [/imath]

SEE HERE

Oh that's another interesting way to do it.