Question #cb13a

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Answer 1 · 2016-10-08T20:31:50

See the explanation section below.

$e^{0.1 t} = 16$ $e^(0.1t) = 16$

Using $ln$ $ln$ for natural logarithm (logarithm base $e$ $e$ ).

$ln (e^{0.1 t}) = ln (16)$ $ln(e^(0.1t)) = ln(16)$

Now use $ln (e^{r}) = r$ $ln(e^r) = r$ to get

$0.1 t = ln (16)$ $0.1t = ln(16)$

Multiply both sides by 10

$t = 10 ln 16$ $t = 10ln16$

We could rewrite this as $ln (16^{10})$ $ln(16^10)$ or as

$10 ln 16 = 10 ln (2^{4}) = 40 ln 2$ $10ln16 = 10 ln(2^4) = 40 ln2$