What is the answer to log_{x}(3)=0.4771 ?

The answer to log_{x}(3)=0.4771 is x=3^{1/(0.4771)}

Solve for x: log_{x}(3)=0.4771

The solution is x=3^{1/(0.4771)}

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lo g_{x} (3) = 0.4771

x = 3^{\frac{1}{0.4771}}

Decimal Notation

x = 10.00102 \dots

Solution steps

lo g_{x} (3) = 0.4771

Apply log rules

\frac{1}{lo g _{3} ( x )} = 0.4771

Multiply both sides by

lo g_{3} (x)

\frac{1}{lo g _{3} ( x )} lo g_{3} (x) = 0.4771 lo g_{3} (x)

Simplify

1 = 0.4771 lo g_{3} (x)

Switch sides

0.4771 lo g_{3} (x) = 1

Divide both sides by

0.4771

lo g_{3} (x) = \frac{1}{0.4771}

Apply log rules

x = 3^{\frac{1}{0.4771}}

Verify Solutions:

x = 3^{\frac{1}{0.4771}}

True

The solution is

x = 3^{\frac{1}{0.4771}}

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What is the answer to log_{x}(3)=0.4771 ?
The answer to log_{x}(3)=0.4771 is x=3^{1/(0.4771)}
Solve for x: log_{x}(3)=0.4771
The solution is x=3^{1/(0.4771)}