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Question : 19 of 86

Marks: +1, -0

If

5^{x+3}=(25)^{3x-4}

then the value of

x

is:

$\;\frac{5}{11}$
$\;\frac{11}{5}$
$\;\frac{11}{3}$
$\;\frac{13}{5}$

Solution:

Concept:

Rewrite both sides with the same base to equate the exponents.

Explanation:

Given

5^{x+3} = (25)^{3x-4}

.

Since

25 = 5^2

, the right side becomes

(5^2)^{3x-4} = 5^{2(3x-4)} = 5^{6x-8}

.

Now the equation is

5^{x+3} = 5^{6x-8}

.

Bases are equal, so equate exponents:

x+3 = 6x-8

.

Bring terms:

3+8 = 6x - x \implies 11 = 5x

.

Thus

x = \frac{11}{5}

.

Answer:

x = \frac{11}{5}

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