What is the answer to log_{x}(0.1)=-1/3 ?

The answer to log_{x}(0.1)=-1/3 is x=1000

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log_{x}(0.1)=-1/3

lo g_{x} (0.1) = - \frac{1}{3}

x = 1000

Solution steps

lo g_{x} (0.1) = - \frac{1}{3}

Apply log rules

\frac{1}{lo g _{0.1} ( x )} = - \frac{1}{3}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 3 = - lo g_{0.1} (x) \cdot 1

Apply log rules

1000 = x

Switch sides

x = 1000

Verify Solutions:

x = 1000

True

The solution is

x = 1000

10 lo g_{10} (x) = 26.5

lo g_{4} (3 x^{2} + 6 x + 7) = 2

ln (ln (5 x)) = 0

lo g_{2} (x^{2} + x - 2) = 2

0.49 = ln (x)

What is the answer to log_{x}(0.1)=-1/3 ?
The answer to log_{x}(0.1)=-1/3 is x=1000
Solve for x: log_{x}(0.1)=-1/3
The solution is x=1000