Find the solution of the exponential equation
$100 (1.05)^{2 t} = 500, 000$
in terms of logarithms, or correct to four decimal places.
$t =$

Answer

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Answer

$t \approx 87.2839$

Steps

Step 1 ：Divide both sides of the equation by 100 to get ${1.05}^{2 t} = 5000$

Step 2 ：Take the natural logarithm (ln) of both sides of the equation to get $2 t \cdot \ln (1.05) = \ln (5000)$

Step 3 ：Divide both sides of the equation by $2 \cdot \ln (1.05)$ to solve for t, which gives $t = \frac{\ln (5000)}{2 \cdot \ln (1.05)}$

Step 4 ：Calculate the value of t to get $t \approx 87.2839$

Step 5 ： $t \approx 87.2839$