Solve for $x$ :
$3^{4 x + 1} = 27^{x + 1}$

Open in App

Solution

Finding the value of $x$
Given,
$3^{4 x + 1} = 27^{x + 1}$
It can be simplified as:
$3^{4 x + 1} = (3 \times 3 \times 3)^{x + 1}$
$3^{4 x + 1} = (3^{3})^{x + 1}$
$3^{4 x + 1} = 3^{3 (x + 1)}$
$3^{4 x + 1} = 3^{3 x + 3}$
We know that :
$a^{m} = a^{2} \Rightarrow m = n$
$∴ 4 x + 1 = 3 x + 3$
$4 x - 3 x = 3 - 1$
$x = 2$

Hence, the value of 𝑥 is 2.

Suggest Corrections

Similar questions

\frac{3}{4} (x - 1) = x - 3

\frac{3}{4} (x - 1) = x - 3

3^{4 x + 1} = (27)^{x + 1}

3^{4 x + 1} = {(27)}^{x + 1}

x

x

\frac{2}{3} (4 x - 1) - [4 x - \frac{1 - 3 x}{2}] = \frac{x - 7}{2}

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program