What is the answer to log_{x}(8)=6 ?

The answer to log_{x}(8)=6 is x=sqrt(2)

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log_{x}(8)=6

lo g_{x} (8) = 6

x = 2

Decimal Notation

x = 1.41421 \dots

Solution steps

lo g_{x} (8) = 6

Apply log rules

\frac{1}{lo g _{8} ( x )} = 6

Multiply both sides by

lo g_{8} (x)

\frac{1}{lo g _{8} ( x )} lo g_{8} (x) = 6 lo g_{8} (x)

Simplify

1 = 6 lo g_{8} (x)

Switch sides

6 lo g_{8} (x) = 1

Divide both sides by

6

lo g_{8} (x) = \frac{1}{6}

Apply log rules

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

lo g_{x} (8) = 2

ln (5 x + 1) + ln (3 x - 1) = ln (8 x - 3)

ln (x + 3) = 0

\frac{ln ( x + 1 )}{2} = ln (x - 5)

- lo g_{10} (x) = 2