SOLUTION: e^x=2^(x-1) solve for x. please explain

Question 241461: e^x=2^(x-1)
solve for x. please explain
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

With the variable in the exponent, we will be using logarithms to solve this. We just need to decide the base of the logarithm we will use. Any base can be used but since the bases for the exponents we have are e and 2, it will be easiest if we use one of these as the base of the logarithm. I'll show both:

Using base e (aka natural logarithms):

Use the property of logarithms, , to move the exponents in front:

Simplify. ln(e) = 1 and multiply out the right side:

Subtract x*ln(2) (to get the x's on the same side of the equation):

Factor out x on the left side:

Divide both sides by (1- ln(2)):
Using base 2 logarithms:

Although the two answers, and , may look different they are actually equal.

You can use a calculator to check. Since very few calculators do base 2 logarithms you will probably need to change the base to find . And, if your calculator does not do natural (ln), then you will have to change the base for also. Hers are the formulas if you want to check:

and

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