How do you solve $4^{- 3 t} = 0.10$ $4^(-3t)=0.10$ ?

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How do you solve $4^{- 3 t} = 0.10$ $4^(-3t)=0.10$ ?

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Answer 1 · 2018-05-19T14:18:47

$4^{- 3 t} = 0.10$ $4^(-3t)=0.10$

Explanation:

$4^{- 3 t} = 0.10$ $4^(-3t)=0.10$
$ln (4^{- 3 t}) = ln (0.10)$ $ln(4^(-3t))=ln(0.10)$
$- 3 t \cdot ln (4) = ln (0.10)$ $-3 t*ln(4)=ln(0.10)$
$t = - \frac{ln (0.10)}{3 \cdot ln (4)}$ $t=- ln(0.10)/(3*ln(4))$

Answer 2 · 2018-05-19T14:19:30

$t = - \frac{log 0.1}{3 log 4} \approx 0.55$ $t=-log0.1/(3log4)~~0.55$

Explanation:

Given: $4^{- 3 t} = 0.1$ $4^(-3t)=0.1$

Take logarithms on both sides.

$log (4^{- 3 t}) = log 0.1$ $log(4^(-3t))=log0.1$

$\Rightarrow - 3 t log 4 = log 0.1$ $=>-3tlog4=log0.1$

$\Rightarrow - 3 t = \frac{log 0.1}{log 4}$ $=>-3t=log0.1/log4$

$t = - \frac{1}{3} \frac{log 0.1}{log 4}$ $t=-1/3log0.1/log4$

$t = - \frac{log 0.1}{3 log 4}$ $t=-log0.1/(3log4)$

$\approx 0.55$ $~~0.55$

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