Write 1 - 2log_{7}x as a single logarithm.

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- Jan 7th 2013, 09:17 AMdzombergLogarithm help need explanation
Write 1 - 2log

_{7}x as a single logarithm.

Thanks! - Jan 7th 2013, 09:27 AMPlatoRe: Logarithm help need explanation
- Jan 7th 2013, 09:28 AMshervladRe: Logarithm help need explanation
- Jan 7th 2013, 09:30 AMrussoRe: Logarithm help need explanation
Hi, this kind of problems involves the use of properties. So you want that expression to be simplified in one logarithm.

First, let's write everything as a logarithm. We know that: so we could say that (in our case). Thus

Then, we have to put, for the second part, "inside" the logarithm. So we also know that: . Finally

We put it altogether (using the substraction of logarithm property of the same base) :