What is the answer to 25*1.005^t=31 ?

The answer to 25*1.005^t=31 is t=(ln(31/25))/(ln(1.005))

Solve for t: 25*1.005^t=31

The solution is t=(ln(31/25))/(ln(1.005))

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25 \cdot 1.00 5^{t} = 31

t = \frac{ln ( \frac{31}{25} )}{ln ( 1.005 )}

Decimal Notation

t = 43.12974 \dots

Solution steps

25 \cdot 1.00 5^{t} = 31

Divide both sides by

25

1.00 5^{t} = \frac{31}{25}

Apply exponent rules

t ln (1.005) = ln (\frac{31}{25})

Solve

t ln (1.005) = ln (\frac{31}{25}) : t = \frac{ln ( \frac{31}{25} )}{ln ( 1.005 )}

t = \frac{ln ( \frac{31}{25} )}{ln ( 1.005 )}

5^{2 x - 1} = 1

2^{2 x} = 4

3^{x} - 3^{x - 1} = 54

9^{x - 3} = 27

7^{x} = 7

What is the answer to 25*1.005^t=31 ?
The answer to 25*1.005^t=31 is t=(ln(31/25))/(ln(1.005))
Solve for t: 25*1.005^t=31
The solution is t=(ln(31/25))/(ln(1.005))