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Popular >

log_{a}(n^a)=n

Solution

lo g_{a} (n^{a}) = n

Solution

n = - \frac{a W ( - \frac{l n ( a )}{a} )}{ln ( a )}

Solution steps

lo g_{a} (n^{a}) = n

If

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

a^{l o g_{a} (n^{a})} = a^{n}

Simplify

a^{l o g_{a} (n^{a})} : n^{a}

n^{a} = a^{n}

Solve

n^{a} = a^{n} : n = - \frac{a W ( - \frac{l n ( a )}{a} )}{ln ( a )}

n = - \frac{a W ( - \frac{l n ( a )}{a} )}{ln ( a )}

Verify Solutions:

n = - \frac{a W ( - \frac{l n ( a )}{a} )}{ln ( a )}

True

The solution is

n = - \frac{a W ( - \frac{l n ( a )}{a} )}{ln ( a )}

Popular Examples

ln(x+3)-ln(x)=ln(6)

ln (x + 3) - ln (x) = ln (6)

log_{3}(x)=3+2log_{x}(9)

lo g_{3} (x) = 3 + 2 lo g_{x} (9)

ln(x+5)+ln(x-1)=2

ln (x + 5) + ln (x - 1) = 2

2log_{10}(x)=-10

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

log_{10}(x)=0.2293300000000…

lo g_{10} (x) = 0.2293300000000 \dots

Frequently Asked Questions (FAQ)

What is the answer to log_{a}(n^a)=n ?
The answer to log_{a}(n^a)=n is n=-(a\W(-(ln(a))/a))/(ln(a))