Question

How do you solve `log_5(x+4)+log_5 8=log_5 64`?

Answer 1

`x=4`

Explanation:

`log_5 (x+4)+log_5 8` = `log_5 8(x+4)`

So `8(x+4)=64`

`x+4=8`
`x=4`

Have you understood the rules of indices?
100 x1000= 100,000
`10^2`x`10^3=10^5`
So in terms of the index numbers
2+3=5
Or
`log_10 2+log_10 3=log_10 5`
Which is the same as
`log_10 (2 times 3) =log_10 5`

Answer 2

Answer is `x=4`.

Explanation:

`log_5 (x+4)+log_5 8=log_5 64`
`:.log(x+4)+log8=log64`
`:.log(x+4)+log2^3=log 2^6`
`:.log(x+4)+3log2=6log2`
`:.log(x+4)=3log2`
`:.log(x+4)=log2^3`
`:.x+4=8`
`:.x=4`. (answer).