What is the answer to log_{n}(8)=3 ?

The answer to log_{n}(8)=3 is n=2

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log_{n}(8)=3

lo g_{n} (8) = 3

n = 2

Solution steps

lo g_{n} (8) = 3

Apply log rules

\frac{1}{lo g _{8} ( n )} = 3

Multiply both sides by

lo g_{8} (n)

\frac{1}{lo g _{8} ( n )} lo g_{8} (n) = 3 lo g_{8} (n)

Simplify

1 = 3 lo g_{8} (n)

Switch sides

3 lo g_{8} (n) = 1

Divide both sides by

3

lo g_{8} (n) = \frac{1}{3}

Apply log rules

n = 2

Verify Solutions:

n = 2

True

The solution is

n = 2

- 7.725 = lo g_{10} (x)

2 lo g_{3} (t) + lo g_{t} (9) = 5

ln (x) + ln^{2} (x) = 3

- 11 + \frac{12}{T} = - 4 ln (T)

lo g_{10} (75) = lo g_{10} (11 x)