What is the answer to 300=1500-1500(0.9)^t ?

The answer to 300=1500-1500(0.9)^t is t=(ln(4/5))/(ln(0.9))

Solve for t: 300=1500-1500(0.9)^t

The solution is t=(ln(4/5))/(ln(0.9))

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300 = 1500 - 1500 (0.9)^{t}

t = \frac{ln ( \frac{4}{5} )}{ln ( 0.9 )}

Decimal Notation

t = 2.11790 \dots

Solution steps

300 = 1500 - 1500 (0.9)^{t}

Switch sides

1500 - 1500 \cdot 0. 9^{t} = 300

Move

1500

to the right side

- 1500 \cdot 0. 9^{t} = - 1200

Divide both sides by

- 1500

0. 9^{t} = \frac{4}{5}

Apply exponent rules

t ln (0.9) = ln (\frac{4}{5})

Solve

t ln (0.9) = ln (\frac{4}{5}) : t = \frac{ln ( \frac{4}{5} )}{ln ( 0.9 )}

t = \frac{ln ( \frac{4}{5} )}{ln ( 0.9 )}

2 \cdot 7^{- 6 x} = 36

e^{2 x} - 1 = 0

a, e^{2 ab} = e^{a}

6^{x} = 0.2 5^{2 x - 1}

4 (2.5)^{2 x} = 4

What is the answer to 300=1500-1500(0.9)^t ?
The answer to 300=1500-1500(0.9)^t is t=(ln(4/5))/(ln(0.9))
Solve for t: 300=1500-1500(0.9)^t
The solution is t=(ln(4/5))/(ln(0.9))