How do you simplify $log_7 9x+log_7x-3log_7 x$ ?

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Answer 1 · 2015-12-12T11:23:35

$log_7(9/x)$

First of all, observe that $3log_7(x)=log_7(x^3)$ . So, your expression becomes

$log_7(9x)+log_7(x)-log_7(x^3)$

Now, the sum of two logarithms is the logarithm of the product:

$log_7(a)+log_7(b)=log_7(ab)$

So,

$color(green)(log_7(9x)+log_7(x))-log_7(x^3)=color(green)(log_7(9x^2))-log_7(x^3)$

And the difference of two logarithms is the logarithm of the ratio:

$log_7(a)-log_7(b)=log_7(a/b)$

So,

$log_7(9x^2)-log_7(x^3) = log_7(9x^2/x^3) = log_7(9/x)$

How do you simplify log_7 9x+log_7x-3log_7 xlog_7 9x+log_7x-3log_7 x?