Question

Please help me I need​

Answer 1

x = - 2

Explanation:

Given

`2^(x+3)` ×
`3^(x+4)` = 18 = 2 × 9 =
`2^(1)` × 3²

Then

`2^(x+3)` =
`2^(1)`

Since bases on both sides are equal, both 2, then equate exponents

x + 3 = 1 ( subtract 3 from both sides )

x = - 2

Then

`2^(-2+3)` =
`2^(1)`

and

`3^(-2+4)` = 3²

18 = 2 × 3²

Answer 2

x=-2

Explanation:

`2 {}^(x + 3) * 3 {}^(x + 4 = 18)`

Apply the Inverse of the Product of Power Rule

If

`x {}^(y) * x {}^(z) = x {}^(y + z)`

This means that

`{x}^(y + z) = {x}^(y) * {x}^(z)`

So in order words,

`(2 {}^(x) * 2 {}^(3) ) * (3 {}^(x) * 3 {}^(4) ) = 18`

`(2 {}^(x) * 8) * (3 {}^(x) * 81) = 18`

Divide both sides by 31 and 8.

We get that

`2 {}^(x) * {3}^(x) = (1)/(36)`

`6 {}^(x) = (1)/(36)`

Take the log of both sides.

`log_(6)( (1)/(36) ) = x`

`6 {}^( - 2) = (1)/(36)`

so

`x = - 2`