Question

If 343^x = 7,find value of x

Answer 1

Answer:

The value of x is 1/3.

Step-by-step explanation:

Given

$\sf {343}^{x} = 7$

To know the value of x first we need to make base in LHS and RHS same.

Prime factorise 343

[tex]\begin{array}{r | l} 7 & 343 \\\cline{1-2} 7 & 49 \\ \cline{1-2} 7 & 7 \\ \cline{1-2} & 1 \end{array}[/tex]

343 = 7 * 7 * 7 = 7³

$\sf \implies {343}^{x} = {7}^{1} \\\\\\ \sf \implies ({7}^{3})^{x} = {7}^{1} \\\\\\ \bf \because 343 = {7}^{3} \\\\\\\\ \sf \implies {7}^{3x} = {7}^{1} \\\\\\ \bf \because ({a}^{m})^{n} = {a}^{mn} \\\\\\ \sf \implies 3x = 1 \\\\\\ \bf \because if \: {a}^{m} = {a}^{n} \: then \: m = n \\\\\\ \sf \implies x = \dfrac{1}{3}$

Therefore the value of x is 1/3.

Answer 2

$\huge{\mathfrak{</p><p><strong>Answer:</strong></p><p>}}$

$\large\sf {(343)}^{x} = 7$

$\large\sf{We \: \: have \: \: to \: \: factoise \: \: 343}$

$\large\sf {(7 \times 7 \times 7)}^{x} = {7}^{1}$

$\huge\bf{Using \: \: formula}$

$\huge\boxed{\orange { {(a ^{m}) }^{n} = {a}^{mn}}}$

$\large\sf{ {7}^{3x} = {7}^{1}}$

$\large\sf{3x = 1}$

$\large\sf{ x = \frac{1}{3}}$

$\huge\boxed{\blue {\frac{1}{3}}}$