Question

${2}^{x + 5} = {2}^{x + 3} + 12$
Find the value of x.
Who can tell me the right answer?????

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Answer 1

$\huge\mathfrak{Bonjour!!}$

$\huge\mathcal\pink{Solutioñ:-}$

☘ Answer:-

☞ x = -1

☘ Step-by-step explanation:-

$2^{x + 5} = 2^{x + 3} + 12$

Move the expression to the left side and change its sign.

↪$2^{x + 5} - 2^{x + 3} = 12$

Now, to make the calculation easier, factor the expression in the LHS.

↪$(2^{2} - 1) \times 2^{x + 3} = 12$

Evaluate the power.

↪$(4 - 1) \times 2^{ x + 3} = 12$

Subtract the numbers.

↪$3 \times 2^{x + 3} = 12$

Divide both sides of the equation by 3.

↪$2^{x + 3} = 4$

Write the number in the RHS in exponential form.

↪$2^{x + 3} = 2 ^{2}$

Now, since the bases are the same, set the exponents equal.

↪$x + 3 = 2$

Move the constant to the right and change it's sign.

↪$x = 2 - 3$

Calculate.

⛄x=-1

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$<marquee>❤Hope it helps❤$