Answer
$t=\dfrac{\log\dfrac{10}{3}}{\log(1.025)^{12}}\approx4.063202$
Work Step by Step
$300(1.025)^{12t}=1000$
Take the $300$ to divide the right side of the equation:
$1.025^{12t}=\dfrac{1000}{300}$
Simplify the right side:
$1.025^{12t}=\dfrac{10}{3}$
Apply $\log$ to both sides of the equation:
$\log1.025^{12t}=\log\dfrac{10}{3}$
Applying the power of a power rule, the left side of the equation can be written like this:
$\log(1.025^{12})^{t}=\log\dfrac{10}{3}$
Take down the exponent $t$ to multiply in front of the $\log$:
$t\log(1.025)^{12}=\log\dfrac{10}{3}$
Solve for $t$:
$t=\dfrac{\log\dfrac{10}{3}}{\log(1.025)^{12}}\approx4.063202$
