What is the answer to solvefor x,log_{x}(64)=-2 ?

The answer to solvefor x,log_{x}(64)=-2 is x= 1/8

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solvefor x,log_{x}(64)=-2

solve for

x, lo g_{x} (64) = - 2

x = \frac{1}{8}

Decimal Notation

x = 0.125

Solution steps

lo g_{x} (64) = - 2

Apply log rules

\frac{1}{lo g _{64} ( x )} = - 2

Multiply both sides by

lo g_{64} (x)

\frac{1}{lo g _{64} ( x )} lo g_{64} (x) = - 2 lo g_{64} (x)

Simplify

1 = - 2 lo g_{64} (x)

Switch sides

- 2 lo g_{64} (x) = 1

Divide both sides by

- 2

lo g_{64} (x) = - \frac{1}{2}

Apply log rules

x = \frac{1}{8}

Verify Solutions:

x = \frac{1}{8}

True

The solution is

x = \frac{1}{8}

3 lo g_{8} (x) - lo g_{x} (64) + 1 = 0

ln (3 x - 10) = 9

ln (3 x - 10) = 3

lo g_{2} (x - 3) + lo g_{2} (x - 9) = 4

2 lo g_{10} (x) = 3 lo g_{5} (4)

What is the answer to solvefor x,log_{x}(64)=-2 ?
The answer to solvefor x,log_{x}(64)=-2 is x= 1/8