What is the answer to log_{a}(sqrt(5))=1 ?

The answer to log_{a}(sqrt(5))=1 is a=5^{1/2}

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log_{a}(sqrt(5))=1

lo g_{a} (5) = 1

a = 5^{\frac{1}{2}}

Decimal Notation

a = 2.23606 \dots

Solution steps

lo g_{a} (5) = 1

Apply log rules

\frac{ln ( 5 )}{ln ( a )} = 1

Multiply both sides by

ln (a)

\frac{ln ( 5 )}{ln ( a )} ln (a) = 1 \cdot ln (a)

Apply log rules

5^{\frac{1}{2}} = a

Switch sides

a = 5^{\frac{1}{2}}

Verify Solutions:

a = 5^{\frac{1}{2}}

True

The solution is

a = 5^{\frac{1}{2}}

x, 0.35 = lo g_{10} (x)

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

lo g_{10} (x) = - 0.91

8 = 8.5 + lo g_{10} (x)

x, 2 lo g_{3} (- x + 1) = 6

What is the answer to log_{a}(sqrt(5))=1 ?
The answer to log_{a}(sqrt(5))=1 is a=5^{1/2}
Solve for a: log_{a}(sqrt(5))=1
The solution is a=5^{1/2}