Logarithms

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 10^x.

 

10^log(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