What is the answer to log_{x}(1000)=3 ?

The answer to log_{x}(1000)=3 is x=10

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log_{x}(1000)=3

lo g_{x} (1000) = 3

x = 10

Solution steps

lo g_{x} (1000) = 3

Apply log rules

\frac{1}{lo g _{1000} ( x )} = 3

Multiply both sides by

lo g_{1000} (x)

\frac{1}{lo g _{1000} ( x )} lo g_{1000} (x) = 3 lo g_{1000} (x)

Simplify

1 = 3 lo g_{1000} (x)

Switch sides

3 lo g_{1000} (x) = 1

Divide both sides by

3

lo g_{1000} (x) = \frac{1}{3}

Apply log rules

x = 10

Verify Solutions:

x = 10

True

The solution is

x = 10

lo g_{2} (2^{x + 1} - 322) = x

ln (y - 1) = 1 + ln (3 y + 2)

lo g_{3} (x + 1) = 3

lo g_{3} (2 x - 5) = 2

lo g_{10} (5) + lo g_{10} (x) = 2