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

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) (Show Source): You can put this solution on YOUR website!
Your first step is flawless!
Now apply the Product Rule for logarithms:
= 3 Simplify.
Rewrite this in exponential form: means
Simplify and solve for x.
Add 8 to both sides.
Divide both sides by 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: Apply this to your problem:
Substitute x = 4.
Use your calculator.
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