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

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

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log_{b}(1000)=3

lo g_{b} (1000) = 3

b = 10

Solution steps

lo g_{b} (1000) = 3

Apply log rules

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

Multiply both sides by

lo g_{1000} (b)

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

Simplify

1 = 3 lo g_{1000} (b)

Switch sides

3 lo g_{1000} (b) = 1

Divide both sides by

3

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

Apply log rules

b = 10

Verify Solutions:

b = 10

True

The solution is

b = 10

0.912 = ln (x^{2})

lo g_{a} (2048) = 11

ln (3) + ln (2 x + 5) = 2 ln (x + 2)

lo g_{20} (x) = 1 + lo g_{20} (10)

2 lo g_{10} (x + 5) - lo g_{3} (9) = 2