What is the answer to log_{x}(2)=0.301 ?

The answer to log_{x}(2)=0.301 is x=8*2^{97/301}

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log_{x}(2)=0.301

lo g_{x} (2) = 0.301

x = 8 \cdot 2^{\frac{97}{301}}

Decimal Notation

x = 10.00229 \dots

Solution steps

lo g_{x} (2) = 0.301

Apply log rules

\frac{1}{lo g _{2} ( x )} = 0.301

Multiply both sides by

lo g_{2} (x)

\frac{1}{lo g _{2} ( x )} lo g_{2} (x) = 0.301 lo g_{2} (x)

Simplify

1 = 0.301 lo g_{2} (x)

Switch sides

0.301 lo g_{2} (x) = 1

Multiply both sides by

1000

301 lo g_{2} (x) = 1000

Divide both sides by

301

lo g_{2} (x) = \frac{1000}{301}

Apply log rules

x = 8 \cdot 2^{\frac{97}{301}}

Verify Solutions:

x = 8 \cdot 2^{\frac{97}{301}}

True

The solution is

x = 8 \cdot 2^{\frac{97}{301}}

lo g_{e} (x) + lo g_{e} (x + 2) = 3

y, ln (y) = ln (x) + 2

lo g_{10} (x) + lo g_{10} (x + 10) = 3

ln (ln (x - 1)) = e

lo g_{10} (x) = 1 + lo g_{10} (3 x - 4)

What is the answer to log_{x}(2)=0.301 ?
The answer to log_{x}(2)=0.301 is x=8*2^{97/301}
Solve for x: log_{x}(2)=0.301
The solution is x=8*2^{97/301}