SOLUTION: Please help me solve this problem: Solve for x and round to the nearest hundredth 4^3+x=30 Please show calculation steps. Thank you.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help me solve this problem: Solve for x and round to the nearest hundredth 4^3+x=30 Please show calculation steps. Thank you.      Log On


   

Question 1006793: Please help me solve this problem:
Solve for x and round to the nearest hundredth
4^3+x=30
Please show calculation steps. Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming the equation is 4%5E%283%2Bx%29=30


4%5E%283%2Bx%29=30 Given equation.


Ln%284%5E%283%2Bx%29%29=Ln%2830%29 Apply natural logs to both sides.


%283%2Bx%29%2ALn%284%29=Ln%2830%29 Use rule 3


3%2ALn%284%29%2Bx%2ALn%284%29=Ln%2830%29 Distribute.


x%2ALn%284%29=Ln%2830%29-3%2ALn%284%29 Subtract 3%2ALn%284%29 from both sides.


x=%28Ln%2830%29-3%2ALn%284%29%29%2F%28Ln%284%29%29 Divide both sides by Ln%284%29. This is the exact solution.


x=-0.54655470219574 Use a calculator to evaluate the expression %28Ln%2830%29-3%2ALn%284%29%29%2F%28Ln%284%29%29.


x=-0.55 Round to the nearest hundredth.


Final Answer: -0.55