Question

4. question (d) and (c)​

Answer 1

Solution :-

First we need to know about exponents :-

$x^0 = 1$

$\left( x^m\right)^n = x^{mn}$

$x^m \times x^n = x^{m + n}$

$x^m \div x^n = x^{m - n}$

Now :-

(c)

$4^{x+1} = 1$

Via converting the base to 4

$4^{x+1} = 4^0$

Now as base are same

→ x + 1 = 0

→ x = -1

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(d)

$2^{2x+2} = 8^{x+1}$

Now as 8 = 2³

$2^{2x + 2} = \left( 2^3\right)^{x+1}\\\\ \implies 2^{2x+2} = 2^{3x + 3}$

Now as bases are Same

→ 2x + 2 = 3x + 3

→ 3x - 2x = 2 - 3

→ x = -1