Question
Find $x$.
$2^{3x}= 8^{2x+1}$
$2^{3x}= 8^{2x+1}$
✓
Answer
We have, $2^{3x}= 8^{2x+1}$
$\Rightarrow 2^{3x}= (2^3)^{2x+1}$
$\Rightarrow 2^{3x}= (2)6x+3$ $[\because(\text{a}^{\text{m}})^{\text{n}}=(\text{a})^{\text{m}\times\text{n}}]$
On compairing the powers of $2$, we get
$3x = 6x + 3$
$\Rightarrow x = -1$
$\Rightarrow 2^{3x}= (2^3)^{2x+1}$
$\Rightarrow 2^{3x}= (2)6x+3$ $[\because(\text{a}^{\text{m}})^{\text{n}}=(\text{a})^{\text{m}\times\text{n}}]$
On compairing the powers of $2$, we get
$3x = 6x + 3$
$\Rightarrow x = -1$
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