What is the answer to 0.45039(1.03)^n=(1.03)^n-1 ?

The answer to 0.45039(1.03)^n=(1.03)^n-1 is n=-(ln(0.54961))/(ln(1.03))

Solve for n: 0.45039(1.03)^n=(1.03)^n-1

The solution is n=-(ln(0.54961))/(ln(1.03))

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0.45039 (1.03)^{n} = (1.03)^{n} - 1

n = - \frac{ln ( 0.54961 )}{ln ( 1.03 )}

Decimal Notation

n = 20.24934 \dots

Solution steps

0.45039 (1.03)^{n} = (1.03)^{n} - 1

Move

1.0 3^{n}

to the left side

- 0.54961 \cdot 1.0 3^{n} = - 1

Divide both sides by

- 0.54961

1.0 3^{n} = \frac{1}{0.54961}

Apply exponent rules

n ln (1.03) = ln (\frac{1}{0.54961})

Solve

n ln (1.03) = ln (\frac{1}{0.54961}) : n = - \frac{ln ( 0.54961 )}{ln ( 1.03 )}

n = - \frac{ln ( 0.54961 )}{ln ( 1.03 )}

8^{x - 1} = 512

4^{2 x - 1} = \frac{1}{32}

\frac{2 5 ^{x}}{5 ^{x + 1}} = 5^{- 3 x}

(5)^{3 x - 1} = 1

0 = 2 e^{- x} x - e^{- x} x^{2}

What is the answer to 0.45039(1.03)^n=(1.03)^n-1 ?
The answer to 0.45039(1.03)^n=(1.03)^n-1 is n=-(ln(0.54961))/(ln(1.03))
Solve for n: 0.45039(1.03)^n=(1.03)^n-1
The solution is n=-(ln(0.54961))/(ln(1.03))