What is the answer to 6^n-9=0 ?

The answer to 6^n-9=0 is n=(2ln(3))/(ln(6))

The solution is n=(2ln(3))/(ln(6))

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6^n-9=0

6^{n} - 9 = 0

n = \frac{2 ln ( 3 )}{ln ( 6 )}

Decimal Notation

n = 1.22629 \dots

Solution steps

6^{n} - 9 = 0

Add

9

to both sides

6^{n} - 9 + 9 = 0 + 9

Simplify

6^{n} = 9

Apply exponent rules

n ln (6) = ln (9)

Solve

n ln (6) = ln (9) : n = \frac{2 ln ( 3 )}{ln ( 6 )}

n = \frac{2 ln ( 3 )}{ln ( 6 )}

y, x e^{y} + y e^{x} = 3

4^{x + 1} = 8^{2 x + 3}

(1000) 1.0 5^{3 x} = 3000

4 9^{x} = 21

320000 = 250342 e^{0.012 x}