1. if 4e^(2-x)=128, find x, giving this answer in exact form.
2. solve the equation loge(3x+5)-loge(2)=2 for x.
3. solve for x given that log2(x)=y+log2(z). State restrictions to parameters.
4. If loge(x)=a, then e^2a+3e^a-2e^-a is equal to?
1. if 4e^(2-x)=128, find x, giving this answer in exact form.
2. solve the equation loge(3x+5)-loge(2)=2 for x.
3. solve for x given that log2(x)=y+log2(z). State restrictions to parameters.
4. If loge(x)=a, then e^2a+3e^a-2e^-a is equal to?
1. First divide both sides by 4 to give e^(2-x) = 32. Then take logarithms.
2. Use the rule log(a) - log(b) = log(a/b) to simplify the left hand side, before exponentiating both sides.
3. Use the fact that if log_a(m) = n then m = a^n to solve for x. What restrictions do you know of when dealing with logarithms and exponentials?
4. Hints: e^(2a) = (e^a)^2, e^(-a) = 1/e^a.