What is the answer to solvefor a,log_{ab}(a)=3 ?

The answer to solvefor a,log_{ab}(a)=3 is a=e^{-(3ln(b))/2} {b>0}

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solvefor a,log_{ab}(a)=3

solve for

a, lo g_{ab} (a) = 3

a = e^{- \frac{3 l n ( b )}{2}} {b > 0}

Solution steps

lo g_{ab} (a) = 3

Apply log rules

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

Multiply both sides by

ln (ab)

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

Simplify

ln (a) = 3 ln (ab)

Apply log rules

a = e^{- \frac{3 l n ( b )}{2}}

Verify Solutions:

a = e^{- \frac{3 l n ( b )}{2}} {b > 0}

The solution is

a = e^{- \frac{3 l n ( b )}{2}} {b > 0}

lo g_{0.1} (x) = - 6

lo g_{\frac{1}{2}} (x + 1) = - 3

lo g_{5} (x) = 10

lo g_{10} (x + 2) = 2 - x

lo g_{b} (b) = 1

What is the answer to solvefor a,log_{ab}(a)=3 ?
The answer to solvefor a,log_{ab}(a)=3 is a=e^{-(3ln(b))/2} {b>0}