Question

If 2⁴×2⁵ = 2^x-1 the find the value of x

Answer 1

★ Solution :-

We need to find the value of $\mathtt x$ in

• $\sf 2^4 \times 2^5 = 2^{x-1}$

Simplifying the given question ,

$\sf \leadsto 2^4\times 2^5 = 2^{x-1}$

$\sf\leadsto 2^{\big(4+5\big)}=2^{x-1}$

$\rm\big[\because a^m\times a^n = a^{\big(m+n\big)}\big]$

$\sf\leadsto 2^9 = 2^{x-1}$

$\sf\leadsto x - 1 = 9$

$\rm\big[\because a^m = a^n \implies m=n\big]$

$\sf\leadsto x = 9 + 1$

$\bf \leadsto x = 10$

$\rule{200}2$

★ Verification :-

Substituting the value of x in the given question , if LHS = RHS , our answer is correct.

$\hookrightarrow \tt 2^4 \times 2^5 = 2^{x-1}$

$\hookrightarrow \tt 2^9 = 2^{x - 1}$

Now , taking RHS and substituting the value of $\tt x$

$\hookrightarrow \tt 2^{10-1}$

$\hookrightarrow \tt 2^9$

Now , comparing with LHS

2⁹ = 2⁹

• LHS = RHS

Hence , verified !

Answer 2

Answer:

✡ Given ✡

$\leadsto$ 2⁴ × 2⁵ = $\sf{2^{x-1}}$

✡ To Find ✡

$\leadsto$ What is the value of x

✡ Solution ✡

➡ 2⁴ × 2⁵ = $\sf{2^{x-1}}$

$\implies$ $\sf{2^({4+5}})$ = $\sf{2^{x-1}}$

$\implies$ 2⁹ = $\sf{2^{x-1}}$

$\implies$ x - 1 = 9

$\implies$ x = 9 + 1

$\implies$ x = 10

Step-by-step explanation:

HOPE IT HELP YOU