Consider the following equation $8^{x - 2} = 2^{x + 3}$ , then x is:

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2

4

1

3

answer is D.

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Detailed Solution

Concept: Firstly, we will be taking the lhs of the expression, and then we know that 8 can be written as

2^{3 .}

Now the comparison of LHS and RHS gives us the fact that both have equal bases. Now we can equate their power and solve for x.
In the question, an expression is given, which we have to solve and get the value of x.
Given expression

8^{x - 1} = 2^{x + 3}

Considering the LHS of expression.
We get to know that

8 = 2 \times 2 \times 2 = 23

So we can write,

8^{x - 1} = 2^{3 (x - 1)}

Now we will put

2^{3 (x - 1)}

in place of

2^{3 (x - 1)}

n place of

8^{(x - 1)}

in the expression given.

8^{x - 1} = 2^{x + 3}

2^{3 (x - 1)} = 2^{x + 3}

By exponents laws RHS and LHS has same base, now we can equate the powers of LHS and RHS, we get

3 (x - 1) = x + 3

Simplifying the expression and we will get the value of x.

3 x - 3 = x + 3

3 x - x = 3 + 3

2 x = 6

x = \frac{6}{2} = 3

here we got the value

x = 3

Hence, the correct answer is option 4.
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