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Question : 69 of 86

Marks: +1, -0

3^{3x-4} 2^{x+5}=3^{5} 2^{8}

Find the value of

x

1
3
$\frac{1}{3}$
0

Solution:

Concept:

Equate exponents of the same base on both sides.

Explanation:

Given

3^{3x-4} \cdot 2^{x+5} = 3^5 \cdot 2^8

.

For base

3

, equate exponents:

3x-4 = 5

.

Solving:

3x = 9

, so

x = 3

.

For base

2

, equate exponents:

x+5 = 8

.

Solving:

x = 3

.

Both give the same value, confirming the solution.

Answer:

x = 3

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