What is the answer to log_{a}(729)=3 ?

The answer to log_{a}(729)=3 is a=9

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log_{a}(729)=3

lo g_{a} (729) = 3

a = 9

Solution steps

lo g_{a} (729) = 3

Apply log rules

\frac{1}{lo g _{729} ( a )} = 3

Multiply both sides by

lo g_{729} (a)

\frac{1}{lo g _{729} ( a )} lo g_{729} (a) = 3 lo g_{729} (a)

Simplify

1 = 3 lo g_{729} (a)

Switch sides

3 lo g_{729} (a) = 1

Divide both sides by

3

lo g_{729} (a) = \frac{1}{3}

Apply log rules

a = 9

Verify Solutions:

a = 9

True

The solution is

a = 9

lo g_{2} (y) = 0

lo g_{2} (y) = 4

lo g_{2} (y) = 7

lo g_{2} (4 x) = lo g_{2} (8)

ln (\frac{x}{5}) + 3 = 5.3