What is the answer to log_{x}(0.5)=-1 ?

The answer to log_{x}(0.5)=-1 is x=2

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log_{x}(0.5)=-1

lo g_{x} (0.5) = - 1

x = 2

Solution steps

lo g_{x} (0.5) = - 1

Apply log rules

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

Multiply both sides by

lo g_{0.5} (x)

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

Apply log rules

2 = x

Switch sides

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

lo g_{3} (x + 2) = - 4

lo g_{4} (x - 6) + 1 = 3 - lo g_{4} (x)

y, ln (x^{2} + y^{2} - 1) = 0

lo g_{x + 8} (2 x^{2} - 5 x - 8) = 2

lo g_{x} (x) = 1