What is the answer to log_{x}(5)=-3 ?

The answer to log_{x}(5)=-3 is x= 1/(\sqrt[3]{5)}

Solve for x: log_{x}(5)=-3

The solution is x= 1/(\sqrt[3]{5)}

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lo g_{x} (5) = - 3

Decimal Notation

x = 0.58480 \dots

Solution steps

lo g_{x} (5) = - 3

Apply log rules

\frac{1}{lo g _{5} ( x )} = - 3

Multiply both sides by

lo g_{5} (x)

\frac{1}{lo g _{5} ( x )} lo g_{5} (x) = - 3 lo g_{5} (x)

Simplify

1 = - 3 lo g_{5} (x)

Switch sides

- 3 lo g_{5} (x) = 1

Divide both sides by

- 3

lo g_{5} (x) = - \frac{1}{3}

Apply log rules

Verify Solutions:

True

The solution is

2 ln (x) = 4

y, lo g_{7} (y) = x

2 lo g_{2} (x) - lo g_{2} (5) = 1

ln (x) = 7.94

lo g_{3} (3 b) + lo g_{3} (b) = 2

What is the answer to log_{x}(5)=-3 ?
The answer to log_{x}(5)=-3 is x= 1/(\sqrt[3]{5)}
Solve for x: log_{x}(5)=-3
The solution is x= 1/(\sqrt[3]{5)}