Question

5^2x+3=25^-3 exponential equation
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Answer 1

Given:

The equation:-

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

What To Find:

We have to find and solve the equation.

How To Find:

1. Make the bases same.
2. Solve the exponents.

Solution:

• Making the base same.

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

25 can also be written as 5²,

⇒ $\bf{5^{2x+3} = 5^{2 \times -3}}$

• Solving the exponents.

$\bf{5^{2x+3} = 5^{2 \times -3}}$

Since the bases are same we will write it as,

⇒ 2x + 3 = 2 × -3

Multiply 2 by -3,

⇒ 2x + 3 = -6

Take 3 to RHS,

⇒ 2x = -6 - 3

Subtract 3 from -6,

⇒ 2x = -9

Take 2 to RHS,

⇒ $\bf{x = \dfrac{-9}{2}}}$

Divide -9 by 2,

⇒ x = -4.5

∴ Thus, x = -4.5.

Answer 2

Solution :

= 5^2x + 3 = 25^-3

= 5^2x + 3 = 5² × -3

= 2x + 3 = 2 × -3

= 2x + 3 = -6

= 2x = -6 - 3

= 2x = -9

= x = -9/2

= x = -4.5 ans.