What is the answer to 5000=3^{n-1} ?

The answer to 5000=3^{n-1} is n=(ln(5000))/(ln(3))+1

Solve for n: 5000=3^{n-1}

The solution is n=(ln(5000))/(ln(3))+1

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5000 = 3^{n - 1}

n = \frac{ln ( 5000 )}{ln ( 3 )} + 1

Decimal Notation

n = 8.75268 \dots

Solution steps

5000 = 3^{n - 1}

Apply exponent rules

ln (5000) = (n - 1) ln (3)

Solve

ln (5000) = (n - 1) ln (3) : n = \frac{ln ( 5000 )}{ln ( 3 )} + 1

n = \frac{ln ( 5000 )}{ln ( 3 )} + 1

1 6^{2 x - 1} = 6 4^{x + 1}

4^{x} = 8

1.618 = 2^{x}

\frac{1}{2} \cdot 2^{(x - 3)} = 32

5^{n + 1} = \frac{1}{125}

What is the answer to 5000=3^{n-1} ?
The answer to 5000=3^{n-1} is n=(ln(5000))/(ln(3))+1
Solve for n: 5000=3^{n-1}
The solution is n=(ln(5000))/(ln(3))+1