What is the answer to log_{x}(8)=0.5 ?

The answer to log_{x}(8)=0.5 is x=64

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log_{x}(8)=0.5

lo g_{x} (8) = 0.5

x = 64

Solution steps

lo g_{x} (8) = 0.5

Apply log rules

\frac{1}{lo g _{8} ( x )} = 0.5

Multiply both sides by

lo g_{8} (x)

\frac{1}{lo g _{8} ( x )} lo g_{8} (x) = 0.5 lo g_{8} (x)

Simplify

1 = 0.5 lo g_{8} (x)

Switch sides

0.5 lo g_{8} (x) = 1

Divide both sides by

0.5

lo g_{8} (x) = 2

Apply log rules

x = 64

Verify Solutions:

x = 64

True

The solution is

x = 64

lo g_{x} (49) = lo g_{7} (343) - 1

9 = 10 lo g_{10} (x)

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

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

lo g_{10} (x) = 1.8965