What is the answer to log_{a}(4)=-1 ?

The answer to log_{a}(4)=-1 is a= 1/4

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log_{a}(4)=-1

lo g_{a} (4) = - 1

a = \frac{1}{4}

Decimal

a = 0.25

Solution steps

lo g_{a} (4) = - 1

Apply log rules

\frac{1}{lo g _{4} ( a )} = - 1

Multiply both sides by

lo g_{4} (a)

\frac{1}{lo g _{4} ( a )} lo g_{4} (a) = - 1 \cdot lo g_{4} (a)

Simplify

1 = - lo g_{4} (a)

Move

lo g_{4} (a)

to the left side

1 + lo g_{4} (a) = 0

Move

1

to the right side

lo g_{4} (a) = - 1

Apply log rules

a = \frac{1}{4}

Verify Solutions:

a = \frac{1}{4}

True

The solution is

a = \frac{1}{4}

lo g_{10} (x^{2}) = 2

4 u = u^{l o g_{2} (u)}

x, lo g_{2} (3 x + 5) = z

\frac{2}{3} lo g_{10} (x) = 6

20 lo g_{10} (x) = 6