Solving logarithms of a difference base.

**oryxncrake** · July 22nd 2009, 02:00 PM

How do I solve for x of a logarithm that has two different base numbers?

For example:

log5 (x - 4) = log7x

Can you show me the steps?

Thanks.

**pickslides** · July 22nd 2009, 02:14 PM

You can use the identity $log_bx = \frac{log_ax}{log_ab}$

In your case you can change $log_7x$ to base 5 as follows

$log_7x = \frac{log_5x}{log_57}$

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