What is the answer to 2187=(3^n-1)/2 ?

The answer to 2187=(3^n-1)/2 is n=(ln(4375))/(ln(3))

Solve for n: 2187=(3^n-1)/2

The solution is n=(ln(4375))/(ln(3))

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2187 = \frac{3 ^{n} - 1}{2}

n = \frac{ln ( 4375 )}{ln ( 3 )}

Decimal

n = 7.63113 \dots

Solution steps

2187 = \frac{3 ^{n} - 1}{2}

Multiply both sides by

2

2187 \cdot 2 = \frac{3 ^{n} - 1}{2} \cdot 2

Simplify

4374 = 3^{n} - 1

Switch sides

3^{n} - 1 = 4374

Move

1

to the right side

3^{n} = 4375

Apply exponent rules

n ln (3) = ln (4375)

Solve

n ln (3) = ln (4375) : n = \frac{ln ( 4375 )}{ln ( 3 )}

n = \frac{ln ( 4375 )}{ln ( 3 )}

x + 1 100 = 1

10 = 95 \cdot 0.91 4^{x}

5^{t} = 7

e^{x} + e^{3 x} = 1

4^{- x + 3} = 8

What is the answer to 2187=(3^n-1)/2 ?
The answer to 2187=(3^n-1)/2 is n=(ln(4375))/(ln(3))
Solve for n: 2187=(3^n-1)/2
The solution is n=(ln(4375))/(ln(3))