What is the answer to log_{a}(sqrt(3))=4 ?

The answer to log_{a}(sqrt(3))=4 is a=e^{(ln(3))/8}

Solve for a: log_{a}(sqrt(3))=4

The solution is a=e^{(ln(3))/8}

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lo g_{a} (3) = 4

a = e^{\frac{l n ( 3 )}{8}}

Decimal Notation

a = 1.14720 \dots

Solution steps

lo g_{a} (3) = 4

Apply log rules

\frac{ln ( 3 )}{ln ( a )} = 4

Multiply both sides by

ln (a)

\frac{ln ( 3 )}{ln ( a )} ln (a) = 4 ln (a)

Apply log rules

a = e^{\frac{l n ( 3 )}{8}}

Verify Solutions:

a = e^{\frac{l n ( 3 )}{8}}

True

The solution is

a = e^{\frac{l n ( 3 )}{8}}

lo g_{7} (x) + lo g_{8} (x) = 1

ln (x + 7) = 2

2 lo g_{8} (5) = lo g_{8} (x)

lo g_{e} (x^{2}) + lo g_{7} (x) = 2

0.48 = lo g_{10} (x)

What is the answer to log_{a}(sqrt(3))=4 ?
The answer to log_{a}(sqrt(3))=4 is a=e^{(ln(3))/8}
Solve for a: log_{a}(sqrt(3))=4
The solution is a=e^{(ln(3))/8}