Question

Solve: log 3 (3x) + log 3 (3) = 5

Answer 1

Answer: x=27

Explanation:

Assumption the 3's are the bases

`log_(3) 3x +log_(3) 3=5` >combine using multiplication log rule (logs with

same base, that are being added can be

combined with multiplication)

`log_(3)( 3x)(3) =5\\` >simplify

`log_(3)( 9x) =5\\` >rewrite into exponent form

`3^(5) = 9x` >simplify

243 = 9x

x=27

Answer 2

x = 27

Explanation:

using the rules of logarithms

•
`log_(b)` b = 1

•
`log_(b)` x = n ⇒ x =
`b^(n)`

then

`log_(3)` (3x) +
`log_(3)` 3 = 5

`log_(3)` (3x) + 1 = 5 ( subtract 1 from both sides )

`log_(3)` (3x) = 4

3x =
`3^(4)` = 81 ( divide both sides by 3 )

x = 27