SOLUTION: Solve for x. Round to the nearest hundredth. 3*4^x-1 + 7=316

Algebra ->  Exponents -> SOLUTION: Solve for x. Round to the nearest hundredth. 3*4^x-1 + 7=316      Log On


   

Question 1194296: Solve for x. Round to the nearest hundredth.
3*4^x-1 + 7=316
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

It appears the equation is 3%2A4%5E%28x-1%29%2B7+=+316

If that is the case, then you should use parenthesis to indicate only the "x-1" is the exponent. So you should write 3*4^(x-1)+7 = 316

Here is one way to solve for x.

3%2A4%5E%28x-1%29%2B7+=+316

3%2A4%5E%28x-1%29+=+316-7 Subtract 7 from both sides

3%2A4%5E%28x-1%29+=+309

4%5E%28x-1%29+=+309%2F3 Divide both sides by 3

4%5E%28x-1%29+=+103

log%28%284%5E%28x-1%29%29%29+=+log%28%28103%29%29 Apply the log to both sides so you can pull down the exponent (see the next step)

%28x-1%29log%28%284%29%29+=+log%28%28103%29%29 Pull down the exponent using the rule log(x^y) = y*log(x)

x-1+=+log%28%28103%29%29%2Flog%28%284%29%29 Divide both sides by log(4)

x-1+=+3.343250 Use your calculator. This value is approximate to 6 decimal places.

x+=+3.343250%2B1 Add 1 to both sides

x+=+4.343250

x+=+4.34 Rounding to the nearest hundredth (aka 2 decimal places)

Answer: x+=+4.34