Question

Log2 (10x+5) - log2 5 =5
PLEASE SOLVE AND SHOW WORK
THANKS A TON

Answer 1

Explanation:

`log_(a)`
`x_(1)` -
`log_(a)`
`x_(2)` =
`log_(a)`
`(x_(1) )/(x_(2) )`

`log_(a)` x = b ⇒
`a^(b)` = x

~~~~~~~~~~~~~~

`log_(2) (10x+5)` -
`log_(2) 5` = 5

`log_(2) (10x+5)/(5)` = 5

`(10x+5)/(5)` =
`2^(5)`

10x + 5 = 32 × 5

2x + 1 = 32

x = 15.5

Answer 2

`\sf x =15.5`

Explanation:

`\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=5`

`\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=log_2 (32)`

`\sf log_2\left((10x+5))/(5) =log_2 (32)`

`\sf 2x+1 =32`

`\sf 2x+1 -1=32-1`

`\sf 2x =31`

`\sf x =15.5`