What is the answer to log_{x}(8)=1.5 ?

The answer to log_{x}(8)=1.5 is x=4

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log_{x}(8)=1.5

lo g_{x} (8) = 1.5

x = 4

Solution steps

lo g_{x} (8) = 1.5

Apply log rules

\frac{1}{lo g _{8} ( x )} = 1.5

Multiply both sides by

lo g_{8} (x)

\frac{1}{lo g _{8} ( x )} lo g_{8} (x) = 1.5 lo g_{8} (x)

Simplify

1 = 1.5 lo g_{8} (x)

Switch sides

1.5 lo g_{8} (x) = 1

Multiply both sides by

10

15 lo g_{8} (x) = 10

Divide both sides by

15

lo g_{8} (x) = \frac{2}{3}

Apply log rules

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

5 ln (2 x + 5) - 14 = 16

lo g_{3} (2 X - 6) = 1

lo g_{3} (x - 4) = 4

5 lo g_{5} (x) = \frac{1}{4}

lo g_{a} (81) = 4