What is the answer to 5=1000(1-1/3)^x ?

The answer to 5=1000(1-1/3)^x is x=-(ln(200))/(ln(2/3))

Solve for x: 5=1000(1-1/3)^x

The solution is x=-(ln(200))/(ln(2/3))

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5 = 1000 (1 - \frac{1}{3})^{x}

x = - \frac{ln ( 200 )}{ln ( \frac{2}{3} )}

Solution steps

5 = 1000 (1 - \frac{1}{3})^{x}

Switch sides

1000 (1 - \frac{1}{3})^{x} = 5

Divide both sides by

1000

(1 - \frac{1}{3})^{x} = \frac{1}{200}

Apply exponent rules

x ln (1 - \frac{1}{3}) = ln (\frac{1}{200})

Solve

x ln (1 - \frac{1}{3}) = ln (\frac{1}{200}) : x = - \frac{ln ( 200 )}{ln ( \frac{2}{3} )}

x = - \frac{ln ( 200 )}{ln ( \frac{2}{3} )}

(2)^{x} = 4

4^{3 x - 2} = \frac{1}{2 2}

4^{x} = 2

10 e^{x - 9} = 90

3^{5 x + 2} + 9^{2 x} = 81

What is the answer to 5=1000(1-1/3)^x ?
The answer to 5=1000(1-1/3)^x is x=-(ln(200))/(ln(2/3))
Solve for x: 5=1000(1-1/3)^x
The solution is x=-(ln(200))/(ln(2/3))