Question

Please help me I need​

Answer 1

Answer:

x=-2

Step-by-step explanation:

$2 {}^{x + 3} \times 3 {}^{x + 4 = 18}$

Apply the Inverse of the Product of Power Rule

If

$x {}^{y} \times x {}^{z} = x {}^{y + z}$

This means that

${x}^{y + z} = {x}^{y} \times {x}^{z}$

So in order words,

$(2 {}^{x} \times 2 {}^{3} ) \times (3 {}^{x} \times 3 {}^{4} ) = 18$

$(2 {}^{x} \times 8) \times (3 {}^{x} \times 81) = 18$

Divide both sides by 31 and 8.

We get that

$2 {}^{x} \times {3}^{x} = \frac{1}{36}$

$6 {}^{x} = \frac{1}{36}$

Take the log of both sides.

$log_{6}( \frac{1}{36} ) = x$

$6 {}^{ - 2} = \frac{1}{36}$

so

$x = - 2$

Answer 2

Answer:

x = - 2

Step-by-step 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