Question

Which is a solution for the equation log (2x-1) + log 5=1

Answer 1

`x=(3)/(2)`

Explanation:

When we don't have any base with "log", we assume it to have base 10.

Using the property Log M + Log N = Log(M*N), we can write:

Log (2x-1) + Log 5 = 1

Log ((2x-1)(5)) = 1

We can turn this into exponential form using
`Log_(a) b=x\\a^x=b`

Thus,

`10^1=(2x-1)(5)\\10=10x-5\\10+5=10x\\15=10x\\x=(15)/(10)=(3)/(2)`