Solve for t a=p(1+r)^t

$a = p {(1 + r)}^{t}$

Rewrite the equation as $p {(1 + r)}^{t} = a$ .

$p {(1 + r)}^{t} = a$

Divide each term by $p$ and simplify.

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Divide each term in $p {(1 + r)}^{t} = a$ by $p$ .

$\frac{p {(1 + r)}^{t}}{p} = \frac{a}{p}$

Cancel the common factor of $p$ .

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Cancel the common factor.

$\frac{p {(1 + r)}^{t}}{p} = \frac{a}{p}$

Divide ${(1 + r)}^{t}$ by $1$ .

${(1 + r)}^{t} = \frac{a}{p}$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln ({(1 + r)}^{t}) = \ln (\frac{a}{p})$

Expand $\ln ({(1 + r)}^{t})$ by moving $t$ outside the logarithm.

$t \ln (1 + r) = \ln (\frac{a}{p})$

Divide each term by $\ln (1 + r)$ and simplify.

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Divide each term in $t \ln (1 + r) = \ln (\frac{a}{p})$ by $\ln (1 + r)$ .

$\frac{t \ln (1 + r)}{\ln (1 + r)} = \frac{\ln (\frac{a}{p})}{\ln (1 + r)}$

Cancel the common factor of $\ln (1 + r)$ .

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Cancel the common factor.

$\frac{t \ln (1 + r)}{\ln (1 + r)} = \frac{\ln (\frac{a}{p})}{\ln (1 + r)}$

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{a}{p})}{\ln (1 + r)}$

Solve for t a=p(1+r)^t

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