What is the answer to log_{x}(4)=0.4 ?

The answer to log_{x}(4)=0.4 is x=32

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log_{x}(4)=0.4

lo g_{x} (4) = 0.4

x = 32

Solution steps

lo g_{x} (4) = 0.4

Apply log rules

\frac{1}{lo g _{4} ( x )} = 0.4

Multiply both sides by

lo g_{4} (x)

\frac{1}{lo g _{4} ( x )} lo g_{4} (x) = 0.4 lo g_{4} (x)

Simplify

1 = 0.4 lo g_{4} (x)

Switch sides

0.4 lo g_{4} (x) = 1

Divide both sides by

0.4

lo g_{4} (x) = 2.5

Apply log rules

x = 32

Verify Solutions:

x = 32

True

The solution is

x = 32

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