What is the answer to 9^{n+10}+3=81 ?

The answer to 9^{n+10}+3=81 is n=(ln(78))/(2ln(3))-10

Solve for n: 9^{n+10}+3=81

The solution is n=(ln(78))/(2ln(3))-10

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9^{n + 10} + 3 = 81

n = \frac{ln ( 78 )}{2 ln ( 3 )} - 10

Decimal Notation

n = - 8.01717 \dots

Solution steps

9^{n + 10} + 3 = 81

Move

3

to the right side

9^{n + 10} = 78

Apply exponent rules

(n + 10) ln (9) = ln (78)

Solve

(n + 10) ln (9) = ln (78) : n = \frac{ln ( 78 )}{2 ln ( 3 )} - 10

n = \frac{ln ( 78 )}{2 ln ( 3 )} - 10

3^{- (x - 2)} = \frac{1}{27}

3^{2 x} = 5

\frac{e ^{x} - 3 e ^{- x}}{2} = 1

2^{x} = \frac{1}{128}

e^{x - 1} - 6 = - 2 x - 3

What is the answer to 9^{n+10}+3=81 ?
The answer to 9^{n+10}+3=81 is n=(ln(78))/(2ln(3))-10
Solve for n: 9^{n+10}+3=81
The solution is n=(ln(78))/(2ln(3))-10