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AP ICET 2024 6th May 2024 Shift 1

Question : 172 of 200

Marks: +1, -0

8^{2x-4}=16^{x-2}

x=

Solution:

First, express both sides of the equation in terms of powers of 2:

8=2^3\;\;

and

\;\;16=2^4

Thus, the equation becomes:

(2^3)^{2x-4}= (2^4)^{x-2}.

Simplifying:

2^{3(2x-4)}=2^{4(x-2)}\;\;\Rightarrow\;\;2^{6x-12}=2^{4x-8}.

Since the bases are the same, equate the exponents:

6x-12=4x-8\;\;\Rightarrow\;\;2x=4\;\;\Rightarrow\;\;x=2.

Quick Tip

When solving exponential equations, express both sides in terms of the same base to simplify the comparison of exponents.

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