What is the answer to 1/3 =0.9^n ?

The answer to 1/3 =0.9^n is n=-(ln(3))/(ln(0.9))

Solve for n: 1/3 =0.9^n

The solution is n=-(ln(3))/(ln(0.9))

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\frac{1}{3} = 0. 9^{n}

n = - \frac{ln ( 3 )}{ln ( 0.9 )}

Decimal Notation

n = 10.42717 \dots

Solution steps

\frac{1}{3} = 0. 9^{n}

Apply exponent rules

ln (\frac{1}{3}) = n ln (0.9)

Solve

ln (\frac{1}{3}) = n ln (0.9) : n = - \frac{ln ( 3 )}{ln ( 0.9 )}

n = - \frac{ln ( 3 )}{ln ( 0.9 )}

\frac{( 1 0 ^{x} - 13 \cdot 1 0 ^{- x} )}{3} = 4

e^{x} - x = 3

9^{3} x + 1 = 5^{x} - 2

2^{x} + 2^{x + 1} + 2^{x + 2} = 448

\frac{3 ^{3 x - 2}}{( 3 ^{x + 3} )} = 81

What is the answer to 1/3 =0.9^n ?
The answer to 1/3 =0.9^n is n=-(ln(3))/(ln(0.9))
Solve for n: 1/3 =0.9^n
The solution is n=-(ln(3))/(ln(0.9))