SOLUTION: can you help me on solving this logarithmic equation, and express irrational solutions in exact form log2(5x)=4

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: can you help me on solving this logarithmic equation, and express irrational solutions in exact form log2(5x)=4      Log On


   

Question 963407: can you help me on solving this logarithmic equation, and express irrational solutions in exact form
log2(5x)=4
Found 3 solutions by MathLover1, addingup, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%282%2C%285x%29%29=4.........change to the base 10
log%28%285x%29%29%2Flog%282%29=4
log%28%285x%29%29=4log%282%29
log%28%285x%29%29=log%282%5E4%29
log%28%285x%29%29=log%2816%29...........if log same, then
5x=16
x=16%2F5 exact solution (and it is not an irrational number)

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
log(5x)/log(2)=4 Multiply both sides by log(2):
log(5x)= 4log(2) Let's work on the right side:
4log(2)= log(2^4)= log(16) So now we have:
log(5x)= log(16) Cancel the logarithms by taking exponents on both sides:
5x=16 Divide both sides by 5
x= 16/5


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

can you help me on solving this logarithmic equation, and express irrational solutions in exact form
log2(5x)=4
log+%282%2C+5x%29+=+4 ----- Logarithmic form

5x+=+2%5E4 -------- Exponential form

5x+=+16

x+=+16%2F5, or highlight_green%28x+=+3.2%29