# Thread: [SOLVED] Log equation help,

1. ## [SOLVED] Log equation help,

When solving an equation involving logs, I've gotten this far

4 = Log5x/log625x

four is equal to log (base 5) x over log (base 625) x

I know x is equal to 25. But how do I get to that answer not using guess and check?

2. Originally Posted by jsmith90210
When solving an equation involving logs, I've gotten this far

4 = Log5x/log625x

four is equal to log (base 5) x over log (base 625) x

I know x is equal to 25. But how do I get to that answer not using guess and check?
First,U should know Log 625 X= (log 5 x)/(log 5 625) ,So U can solve it.

3. Originally Posted by jsmith90210
[SIZE=2]four is equal to log (base 5) x over log (base 625) x
Since 625 = 5^4, then the change-of-base formula can prove helpful:

. . . . . $\log_{625}(x)\, =\, \frac{\log_5(x)}{\log_5(625)}\,=\,\frac{\log_5(x)} {\log_5(5^4)}$

Then apply a log rule and the definition of logs to convert $\log_5(5^4)$ to just "4".

4. ## Excuse my ignorance

Excuse my ignorance, but how does that help me.

Of course

which would leave:

(Log(base 5) x) OVER (log(base 5) x / 4) on one side

and 4 on the other side

of course 4 = 4

5. ## Solved

Nevermind, I should have seen this. The answer is actually

x = 5^n, where n > 1