Use logarithms to solve the equation for t. Please round the answer to four decimal places.

Question

Use logarithms to solve the equation for t. Please round the answer to four decimal places. ​  ​

Quizplus · Accepted Answer

Start by using logarithms to isolate the variable t:

$log_{10}(t+1) + 2log_{10}(t-2) = 2$

$log_{10}(t+1) + log_{10}(t-2)^2 = 2$

$log_{10}(t+1)(t-2)^2 = 10^2$

$(t+1)(t-2)^2 = 100$

$(t-2)^2(t+1-3) = 0$

$(t-2)^2(t-2) = 0$

$t = 2$ or $t=3$

Round the answer to four decimal places:

$t\approx2.0000$ or $t\approx3.0000$, but $t=2.0000$ is not possible since it results in a log of zero, which is undefined. Therefore, $t\approx3.0000$ is the only possible solution.

The correct answer choice is D: 11eb651f_cb3f_0b69_b0a1_abf36074280d_TB8255_11.

Use Logarithms to Solve the Equation for T