What is the answer to 8000=500e^{ln(12/5)t} ?

The answer to 8000=500e^{ln(12/5)t} is t=(4ln(2))/(ln(12/5))

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8000=500e^{ln(12/5)t}

8000 = 500 e^{l n (\frac{12}{5}) t}

t = \frac{4 ln ( 2 )}{ln ( \frac{12}{5} )}

Decimal Notation

t = 3.16697 \dots

Solution steps

8000 = 500 e^{l n (\frac{12}{5}) t}

Switch sides

500 e^{l n (\frac{12}{5}) t} = 8000

Divide both sides by

500

e^{l n (\frac{12}{5}) t} = 16

Apply exponent rules

ln (\frac{12}{5}) t = ln (16)

Solve

ln (\frac{12}{5}) t = ln (16) : t = \frac{4 ln ( 2 )}{ln ( \frac{12}{5} )}

t = \frac{4 ln ( 2 )}{ln ( \frac{12}{5} )}

4^{3 x - 5} = \frac{1}{256}

3000 = 3 \cdot 1 0^{x}

x, e^{- I n x} = 0.2

x, c = e^{x} + x y - y^{2}

3 e^{x} = e^{- x}

What is the answer to 8000=500e^{ln(12/5)t} ?
The answer to 8000=500e^{ln(12/5)t} is t=(4ln(2))/(ln(12/5))