Question

Solve the following exponential question:

Answer 1

x = - 0.55 ( 2 dec. places )

Explanation:

Express
`4^(x+2)` as

`4^(x)` . 4² -
`4^(x)` = 7

Factor out
`4^(x)` from each term

`4^(x)` ( 4² - 1) = 7

`4^(x)` × 15 = 7 ( divide both sides by 15)

`4^(x)` =
`(7)/(15)`

Take the log ( base 10 ) of both sides

log
`4^(x)` = log (
`(7)/(15)`), thus

x log 4 = log (
`(7)/(15)` ) ( divide both sides by log 4 )

x = - 0.55