SOLUTION: I need help figuring out which way to proceed to solve this problem. log2(x-2) +5 = 8- log2 4. The 2 is the base of the log. I think I should rewrite as log2(x-2) + log2 4 = 3

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I need help figuring out which way to proceed to solve this problem. log2(x-2) +5 = 8- log2 4. The 2 is the base of the log. I think I should rewrite as log2(x-2) + log2 4 = 3       Log On


   

Question 22747: I need help figuring out which way to proceed to solve this problem.
log2(x-2) +5 = 8- log2 4. The 2 is the base of the log. I think I should rewrite as log2(x-2) + log2 4 = 3 What is the correct way. I think answer is
4(x-2) =2^3 x=4
Thanks
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Your first step is flawless!
log%282%2C%28x-2%29%29%2Blog%282%2C4%29=+3 Now apply the Product Rule for logarithms: log%28b%2CM%29%2Blog%28b%2CN%29+=+log%28b%2C%28MN%29%29
log%282%2C%28x-2%29%29%2Blog%282%2C4%29+=+log%282%2C%284%28x-2%29%29%29 = 3 Simplify.
log%282%2C%284x-8%29%29+=+3 Rewrite this in exponential form: log%28b%2Cx%29+=+y means b%5Ey+=+x
2%5E3+=+4x-8 Simplify and solve for x.
8+=+4x-8 Add 8 to both sides.
16+=+4x Divide both sides by 4.
x+=+4
Check: You could use your calculator but most likely it doesn't have logs to base 2. So, you can change the base of logs from 2 to base 10, which your calculator most-likely can handle.
Change of base from 2 to 10: log%282%2CM%29+=+%28log%2810%2CM%29%29%2Flog%2810%2C2%29 Apply this to your problem:
log%282%2C%284x-8%29%29+=+%28log%2810%2C%284x-8%29%29%29%2Flog%2810%2C2%29 Substitute x = 4.
%28log%2810%2C8%29%29%2Flog%2810%2C2%29+=+3 Use your calculator.