Solve the exponential equation for . Round to the nearest thousandth.
A) 0.217
B) 4.605
C) 273,252.194
D) 2.718
E) 2.000

Question

Solve the exponential equation  for  . Round to the nearest thousandth.
A) 0.217 
B) 4.605 
C) 273,252.194 
D) 2.718 
E) 2.000

Quizplus · Accepted Answer

Taking the natural log of both sides, we get:
ln(11ec1b6e_3c5a_35bc_bbf8_53c5a8ae3d8c_TBX8728_11) = ln(3) + ln(11ec1b6e_3c5a_35bc_bbf8_53c5a8ae3d8c_TBX8728_11) - ln(7)
Let x = ln(11ec1b6e_3c5a_35bc_bbf8_53c5a8ae3d8c_TBX8728_11). Then we have:
x = ln(3) + x - ln(7)
Solving for x:
x = ln(3/7)
Substituting back in for 11ec1b6e_3c5a_35bc_bbf8_53c5a8ae3d8c_TBX8728_11, we get:
11ec1b6e_3c5a_35bd_bbf8_cbb000a4d0a0_TBX8728_11 = e^(ln(3/7)) ≈ 0.4595
Rounding to the nearest thousandth, we get 0.459. Therefore, the answer is choice B.

Solve the Exponential Equation for