How do you solve $2 a^{\frac{t}{3}} = 5$ $2a^(t/3)=5$ ?

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Answer 1 · 2015-12-13T12:15:21

Use a logarithm to remove $t$ $t$ from the exponent and find that
$t = \frac{3 ln (\frac{5}{2})}{ln (a)}$ $t = (3ln(5/2))/ln(a)$

Using the property of logarithms that
$ln (a^{x}) = x ln (a)$ $ln(a^x) = xln(a)$
we have

$2 a^{\frac{t}{3}} = 5$ $2a^(t/3) = 5$

$\Rightarrow a^{\frac{t}{3}} = \frac{5}{2}$ $=> a^(t/3) = 5/2$

$\Rightarrow ln (a^{\frac{t}{3}}) = ln (\frac{5}{2})$ $=> ln(a^(t/3)) = ln(5/2)$

$\Rightarrow \frac{t}{3} ln (a) = ln (\frac{5}{2})$ $=> t/3ln(a) = ln(5/2)$

$\Rightarrow t = \frac{3 ln (\frac{5}{2})}{ln (a)}$ $=> t = (3ln(5/2))/ln(a)$

How do you solve 2a^(t/3)=52at3=5 2a^(t/3)=5?