SOLUTION: Could you please take the time to help me solve this problem: Solve g(x) = 0 for x, if g(x) = log x + log x2 + 8 log x – log x3 – 16. Note that all logarithmic functions are to the

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Could you please take the time to help me solve this problem: Solve g(x) = 0 for x, if g(x) = log x + log x2 + 8 log x – log x3 – 16. Note that all logarithmic functions are to the      Log On


   

Question 106845: Could you please take the time to help me solve this problem: Solve g(x) = 0 for x, if g(x) = log x + log x2 + 8 log x – log x3 – 16. Note that all logarithmic functions are to the base 10. Show your work.
Thank you for helping me
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Solve g(x) = 0 for x, if
g%28x%29=log%28%28x%29%29%2B8%2Alog+x%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16
The original equation is re-written to group like terms.
Here are the logarithm rules for reference
log%28%28a%29%29%2Blog%28%28b%29%29=log+%28%28ab%29%29
log%28%28a%29%29-log%28%28b%29%29=log+%28%28a%2Fb%29%29
k+log%28%28a%29%29+=+log%28%28a%5Ek%29%29
Now let's appply the rules to your equation,
g%28x%29=log%28%28x%29%29%2B8%2Alog+x%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16
g%28x%29=9%2Alog%28%28x%29%29%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16
g%28x%29=log%28%28x%5E9%29%29%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16
g%28x%29=log%28%28x%5E9%2A%28x%5E2%29%2Fx%5E3%29%29-16
g%28x%29=log%28%28x%5E%289%2B2-3%29%29%29-16
g%28x%29=log%28%28x%5E%288%29%29%29-16
When g(x)=0, then
0=log%28%28x%5E%288%29%29%29-16
log%28%28x%5E%288%29%29%29=16
x%5E8=10%5E16
x%5E8=%2810%5E2%29%5E8
x=%2810%5E2%29
highlight%28x=100%29
Check your answer
g%28x%29=log%28%28x%29%29%2B8%2Alog+x%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16
g%28100%29=+log%28100%29%2B8%2Alog%28100%29%2Blog%28100%5E2%29-log%28100%5E3%29-16
0=2%2B8%2A2%2B4-6-16
0=0
Good answer.