What is the answer to 6640=5000(1+0.001)^T ?

The answer to 6640=5000(1+0.001)^T is T=(ln(166/125))/(ln(1.001))

Solve for T: 6640=5000(1+0.001)^T

The solution is T=(ln(166/125))/(ln(1.001))

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6640 = 5000 (1 + 0.001)^{T}

T = \frac{ln ( \frac{166}{125} )}{ln ( 1.001 )}

Decimal Notation

T = 283.81586 \dots

Solution steps

6640 = 5000 (1 + 0.001)^{T}

Switch sides

5000 (1 + 0.001)^{T} = 6640

Divide both sides by

5000

(1 + 0.001)^{T} = \frac{166}{125}

Apply exponent rules

T ln (1 + 0.001) = ln (\frac{166}{125})

Solve

T ln (1 + 0.001) = ln (\frac{166}{125}) : T = \frac{ln ( \frac{166}{125} )}{ln ( 1.001 )}

T = \frac{ln ( \frac{166}{125} )}{ln ( 1.001 )}

3^{(- 2)} \cdot 3^{(2 x)} = 7

e^{x} = 2 x + 1

e^{x} = 2 x + 2

2^{3 x - 4} = 18

3 \cdot (2)^{x - 1} - 2 = 0

What is the answer to 6640=5000(1+0.001)^T ?
The answer to 6640=5000(1+0.001)^T is T=(ln(166/125))/(ln(1.001))
Solve for T: 6640=5000(1+0.001)^T
The solution is T=(ln(166/125))/(ln(1.001))