What is the answer to log_{x}(25)=-1 ?

The answer to log_{x}(25)=-1 is x= 1/25

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log_{x}(25)=-1

lo g_{x} (25) = - 1

x = \frac{1}{25}

Decimal Notation

x = 0.04

Solution steps

lo g_{x} (25) = - 1

Apply log rules

\frac{1}{lo g _{25} ( x )} = - 1

Multiply both sides by

lo g_{25} (x)

\frac{1}{lo g _{25} ( x )} lo g_{25} (x) = - 1 \cdot lo g_{25} (x)

Simplify

1 = - lo g_{25} (x)

Move

lo g_{25} (x)

to the left side

1 + lo g_{25} (x) = 0

Move

1

to the right side

lo g_{25} (x) = - 1

Apply log rules

x = \frac{1}{25}

Verify Solutions:

x = \frac{1}{25}

True

The solution is

x = \frac{1}{25}

lo g_{10} (x - 3) + lo g_{10} (x) = 1

lo g_{9} (5 x - 1) = lo g_{9} (3 x + 7)

lo g_{6} (x - 4) = lo g_{6} (2 x + 8)

ln (x) + ln (x + 3) = ln (20 - 5 x)

ln (x) = 2.3