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

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

Solve for t: 0.1=50(0.9^t)

The solution is t=(ln(0.002))/(ln(0.9))

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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 )}

4 (2^{x}) = 10

e^{- 0.3 t} = 125

35 = 21 + 1079 (e^{- 19028 x})

a^{x} ln (a) = e

e^{x} \cdot x = 0

What is the answer to 0.1=50(0.9^t) ?
The answer to 0.1=50(0.9^t) is t=(ln(0.002))/(ln(0.9))
Solve for t: 0.1=50(0.9^t)
The solution is t=(ln(0.002))/(ln(0.9))