What is the answer to log_{t}(243)=5 ?

The answer to log_{t}(243)=5 is t=3

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log_{t}(243)=5

lo g_{t} (243) = 5

t = 3

Solution steps

lo g_{t} (243) = 5

Apply log rules

\frac{1}{lo g _{243} ( t )} = 5

Multiply both sides by

lo g_{243} (t)

\frac{1}{lo g _{243} ( t )} lo g_{243} (t) = 5 lo g_{243} (t)

Simplify

1 = 5 lo g_{243} (t)

Switch sides

5 lo g_{243} (t) = 1

Divide both sides by

5

lo g_{243} (t) = \frac{1}{5}

Apply log rules

t = 3

Verify Solutions:

t = 3

True

The solution is

t = 3

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