What is the answer to log_{x}(9)=-1 ?

The answer to log_{x}(9)=-1 is x= 1/9

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log_{x}(9)=-1

lo g_{x} (9) = - 1

x = \frac{1}{9}

Decimal Notation

x = 0.11111 \dots

Solution steps

lo g_{x} (9) = - 1

Apply log rules

\frac{1}{lo g _{9} ( x )} = - 1

Multiply both sides by

lo g_{9} (x)

\frac{1}{lo g _{9} ( x )} lo g_{9} (x) = - 1 \cdot lo g_{9} (x)

Simplify

1 = - lo g_{9} (x)

Move

lo g_{9} (x)

to the left side

1 + lo g_{9} (x) = 0

Move

1

to the right side

lo g_{9} (x) = - 1

Apply log rules

x = \frac{1}{9}

Verify Solutions:

x = \frac{1}{9}

True

The solution is

x = \frac{1}{9}

r, d = ln (1 + rs)

ln (r) = - 2

4 ln (x - 1) = - 8

3 lo g_{7} (1) = lo g_{7} (1^{n})

ln (x) = 3.11