SOLUTION: needing help with finding what x equals in this equation 4(2x-7)^5=12

Question 276813: needing help with finding what x equals in this equation
4(2x-7)^5=12
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
To solve for x means to transform the equation so that it has the form
x = something
or
something = x

With your equation, to get the x by itself on one side of the equation, we will need to get rid of the 4, the 2 the -7 and the 5 (not in that order). To get rid of all these we need to "peel away" from the outside. So we start by getting rid of the 4 which is separate from the expression in parentheses and its exponent. We can divide both sides by 4 giving:

Still peeling away from the out side, the 5 is the next to go. We can find the 5th root of each side:

The left side simplifies to:

The next to go is the -7 (since it is separate from the term with x in it). We can just add 7 to each side:

(I put the 7 in front on the right side so that it cannot be thought of as part of the 5th root.) The 2 is the last to go. Divide both sides by 2:

which is the answer to the problem. (If you need a decimal approximation then use your calculator on the right side. To find a 5th root with your calculator, just raise 3 to the 0.2 power (since 5th roots are exponents of 1/5 and 1/5 as a decimal is 0.2).)
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