Question

How do you solve `log_2(x+5)-log_2(2x-1)=5`?

Answer 1

I found: `x=37/63`

Explanation:

We can change the subtraction into a division of arguments and write:
`log_2((x+5)/(2x-1))=5`
then we use the definition of log to get rid of it and write:
`(x+5)/(2x-1)=2^5`
`(x+5)/(2x-1)=32`
rearrange:
`x+5=64x-32`
and:
`63x=37`
so:
`x=37/63`