log(x-2)+log(5)=log(100)
First evaluate the log of 100, which is 2.
log(x-2)+log(5)=2
Now we can combine the logs using the log product rule.
log(5x-10)=2
Since there is no subscript, the base is 10. The inverse of log10(x) is the exponential 10x.
10log(5x-10)=102
The base 10 and the log will cancel each other.
5x-10=100
Next add 10 to both sides
5x=110
Finally divide both sides by 5
x=22
Now to check the work input 22 for x.
log(5(22)-10)=log(100)
log(110-10)=2
log(100)=2
2=2
