What is the answer to 3000=7500(0.9)^{2x} ?

The answer to 3000=7500(0.9)^{2x} is x=(ln(2/5))/(2ln(0.9))

Solve for x: 3000=7500(0.9)^{2x}

The solution is x=(ln(2/5))/(2ln(0.9))

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3000 = 7500 (0.9)^{2 x}

x = \frac{ln ( \frac{2}{5} )}{2 ln ( 0.9 )}

Decimal Notation

x = 4.34835 \dots

Solution steps

3000 = 7500 (0.9)^{2 x}

Switch sides

7500 \cdot 0. 9^{2 x} = 3000

Divide both sides by

7500

0. 9^{2 x} = \frac{2}{5}

Apply exponent rules

2 x ln (0.9) = ln (\frac{2}{5})

Solve

2 x ln (0.9) = ln (\frac{2}{5}) : x = \frac{ln ( \frac{2}{5} )}{2 ln ( 0.9 )}

x = \frac{ln ( \frac{2}{5} )}{2 ln ( 0.9 )}

- 24.9 = lo g_{10} (12 1^{x})

(\frac{1}{5})^{2 x + 1} = 25

(\frac{1}{2})^{2 x} = 4^{3}

e^{x} = 0.01

7^{- 8 a} + 10 = 95

What is the answer to 3000=7500(0.9)^{2x} ?
The answer to 3000=7500(0.9)^{2x} is x=(ln(2/5))/(2ln(0.9))
Solve for x: 3000=7500(0.9)^{2x}
The solution is x=(ln(2/5))/(2ln(0.9))