Solve the equation: {{MATH_162}}. {{CMD_163}} Immediately taking logarithms of both sides will not help here, as the right side has multiple terms. We know that logarithms behave well with products and quotients, but not with sums. Notice that {{MATH_164}}. (This is a common trick that you will likely see many times.) {{ENV_165}} Our equation is really a quadratic equation in {{MATH_166}}. The left-hand side factors as {{MATH_167}}, so we are dealing with {{MATH_168}} For the first factor: {{ENV_169}} From the second factor: {{MATH_170}}. Recall from above that the range of the exponential function is {{MATH_171}}. There is no input to make the output a negative number, so {{MATH_172}} has no solutions. The solution to {{MATH_173}} is {{MATH_174}}. {{CMD_175}} {{CMD_176}}