How do you solve ${(16 + \frac{878}{26})}^{3 t} = 2$ $(16+ \frac { 878} { 26} ) ^ { 3t } = 2$ ?

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How do you solve ${(16 + \frac{878}{26})}^{3 t} = 2$ $(16+ \frac { 878} { 26} ) ^ { 3t } = 2$ ?

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Answer 1 · 2017-11-02T06:28:45

$t = 0.059131198$ $t=0.059131198$

Explanation:

${(16 + \frac{878}{26})}^{3 t} = 2$ $(16+878/26)^(3t)=2$

1) Using the law ${ln m}^{n} = n ln m$ $lnm^n=nlnm$ , take the natural log (ln) of both sides of the equation to prevent the variable from being an exponent.
${ln (16 + \frac{878}{26})}^{3 t} = ln (2)$ $ln(16+878/26)^(3t)=ln(2)$
$(3 t) ln (16 + \frac{878}{26}) = ln (2)$ $(3t)ln(16+878/26)=ln(2)$

2) Isolate $t$ $t$ .
$(3 t) = \frac{ln (2)}{ln (16 + \frac{878}{26})}$ $(3t)=ln(2)/ln(16+878/26)$
$t = \frac{ln (2)}{ln (16 + \frac{878}{26})} \cdot \frac{1}{3}$ $t=ln(2)/ln(16+878/26)*1/3$

3) Solve using a calculator.
$t = 0.059131198$ $t=0.059131198$

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How do you solve ${(16 + \frac{878}{26})}^{3 t} = 2$ $(16+ \frac { 878} { 26} ) ^ { 3t } = 2$ ?

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Explanation:

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How do you solve (16+87826)3t=2(16+ \frac { 878} { 26} ) ^ { 3t } = 2?

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How do you solve ${(16 + \frac{878}{26})}^{3 t} = 2$ $(16+ \frac { 878} { 26} ) ^ { 3t } = 2$ ?