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

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

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log_{x}(243)=5

lo g_{x} (243) = 5

x = 3

Solution steps

lo g_{x} (243) = 5

Apply log rules

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

Multiply both sides by

lo g_{243} (x)

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

Simplify

1 = 5 lo g_{243} (x)

Switch sides

5 lo g_{243} (x) = 1

Divide both sides by

5

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

Apply log rules

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{3} (x - 5) = lo g_{3} (x) - 5

lo g_{2} (x - 1) + lo g_{2} (x + 3) = 1

lo g_{4} (2 - x) = lo g_{16} (13 - 4 x)

ln (x) = 10

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