Does anyone know how to go about solving a problem ln(a) = e^x algebraically? For example, the problem ln(5/4) = e^2x.

My teacher somehow got it to be 2x = ln(5/4) but I don't really understand how she got there. Can anyone explain? Thank you so much!

30 is 6 multiplied by a number y as a equation

James adds two numbers a + b. sally adds the same two numbers but reverse the order b + a what property of addition assures us that james and sally will get the same sum

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?