What is the answer to log_{x}(15)=-1 ?

The answer to log_{x}(15)=-1 is x= 1/15

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log_{x}(15)=-1

lo g_{x} (15) = - 1

x = \frac{1}{15}

Decimal Notation

x = 0.06666 \dots

Solution steps

lo g_{x} (15) = - 1

Apply log rules

\frac{1}{lo g _{15} ( x )} = - 1

Multiply both sides by

lo g_{15} (x)

\frac{1}{lo g _{15} ( x )} lo g_{15} (x) = - 1 \cdot lo g_{15} (x)

Simplify

1 = - lo g_{15} (x)

Move

lo g_{15} (x)

to the left side

1 + lo g_{15} (x) = 0

Move

1

to the right side

lo g_{15} (x) = - 1

Apply log rules

x = \frac{1}{15}

Verify Solutions:

x = \frac{1}{15}

True

The solution is

x = \frac{1}{15}

lo g_{10} (x) + lo g_{10} (x - 3) = 2

lo g_{10} (x) = 1.2

lo g_{12} (x^{2} - x) = 1

lo g_{3} (lo g_{2} (x)) = 2

ln^{2} (x) = 1