What is the answer to log_{a}(6)=0.1436 ?

The answer to log_{a}(6)=0.1436 is a=6^{1/(0.1436)}

Solve for a: log_{a}(6)=0.1436

The solution is a=6^{1/(0.1436)}

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lo g_{a} (6) = 0.1436

a = 6^{\frac{1}{0.1436}}

Decimal Notation

a = 262349.70108 \dots

Solution steps

lo g_{a} (6) = 0.1436

Apply log rules

\frac{1}{lo g _{6} ( a )} = 0.1436

Multiply both sides by

lo g_{6} (a)

\frac{1}{lo g _{6} ( a )} lo g_{6} (a) = 0.1436 lo g_{6} (a)

Simplify

1 = 0.1436 lo g_{6} (a)

Switch sides

0.1436 lo g_{6} (a) = 1

Divide both sides by

0.1436

lo g_{6} (a) = \frac{1}{0.1436}

Apply log rules

a = 6^{\frac{1}{0.1436}}

Verify Solutions:

a = 6^{\frac{1}{0.1436}}

True

The solution is

a = 6^{\frac{1}{0.1436}}

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2 lo g_{10} (x) + 4 = 10

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lo g_{5} (10 b + 10) = lo g_{5} (50)

What is the answer to log_{a}(6)=0.1436 ?
The answer to log_{a}(6)=0.1436 is a=6^{1/(0.1436)}
Solve for a: log_{a}(6)=0.1436
The solution is a=6^{1/(0.1436)}