What is the answer to solvefor t,0.1=50(0.9^t) ?

The answer to solvefor t,0.1=50(0.9^t) is t=(ln(0.002))/(ln(0.9))

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solvefor t,0.1=50(0.9^t)

solve for

t, 0.1 = 50 (0. 9^{t})

t = \frac{ln ( 0.002 )}{ln ( 0.9 )}

Decimal Notation

t = 58.98422 \dots

Solution steps

0.1 = 50 (0. 9^{t})

Switch sides

50 \cdot 0. 9^{t} = 0.1

Divide both sides by

50

0. 9^{t} = 0.002

Apply exponent rules

t ln (0.9) = ln (0.002)

Solve

t ln (0.9) = ln (0.002) : t = \frac{ln ( 0.002 )}{ln ( 0.9 )}

t = \frac{ln ( 0.002 )}{ln ( 0.9 )}

3 e^{x} = 120

4 = 8^{x}

- e^{x + 1} + 5 = 4

e^{e^{x}} = 9

\frac{27}{3 ^{x}} = \frac{1}{81}

What is the answer to solvefor t,0.1=50(0.9^t) ?
The answer to solvefor t,0.1=50(0.9^t) is t=(ln(0.002))/(ln(0.9))