Question

Find value of x if
(I) 25^2x-3=5^2x+3
pls help mates!!!!!
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Answer 1

PLEASE REFER TO THE ATTACHMENT.............☆

Answer 2

Question: Find the value of $x$ if $25^{2x-3}=5^{2x+3}$.

Answer:

The value of $x$ is $9/2$.

Step-by-step explanation:

Recall the laws of the exponents,

(i) $(a^m)^n=a^{mn}$

(ii) $\frac{a^m}{a^n}=a^{m-n}$

(iii) If $a^m=a^n$ then $m=n$.

Consider the given expression as follows:

$25^{2x-3}=5^{2x+3}$

To find: the value of $x$.

Step 1 of 3

Evaluating the left-hand side as follows:

⇒ $25^{2x-3}$

⇒ $(5^2)^{2x-3}$

⇒ $5^{2(2x-3)}$ (From the law of exponents (i))

Further, simplify as follows:

⇒ $5^{4x-6}$

Step 2 of 3

Evaluating the right-hand side as follows:

⇒ $5^{2x+3}$

Step 3 of 3

Putting the left-hand side equals to the right-hand side.

$5^{4x-6}=5^{2x+3}$

Using law of exponents (iii),

⇒ $4x-6=2x+3$

Simplify as follows:

⇒ $4x-2x=3+6$

⇒ $2x=9$

⇒ $x=9/2$

Therefore, the value of $x$ is $9/2$.

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