What is the answer to log_{a}(6)=0.5 ?

The answer to log_{a}(6)=0.5 is a=36

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log_{a}(6)=0.5

lo g_{a} (6) = 0.5

a = 36

Solution steps

lo g_{a} (6) = 0.5

Apply log rules

\frac{1}{lo g _{6} ( a )} = 0.5

Multiply both sides by

lo g_{6} (a)

\frac{1}{lo g _{6} ( a )} lo g_{6} (a) = 0.5 lo g_{6} (a)

Simplify

1 = 0.5 lo g_{6} (a)

Switch sides

0.5 lo g_{6} (a) = 1

Divide both sides by

0.5

lo g_{6} (a) = 2

Apply log rules

a = 36

Verify Solutions:

a = 36

True

The solution is

a = 36

lo g_{10} (x) = - 0.74

lo g_{3} (3 x) - lo g_{3} (x + 1) = 2

\frac{3}{4} lo g_{7} (x) = 5

\frac{9}{8} lo g_{2} (x) = - 7

2 ln (x) = ln (x)