Question

49 raised to x = 343 raised to 2x-3

Answer 1

${49}^{x} = {343}^{2x - 3} \\ {( {7}^{2} )}^{x} = {( {7}^{3} )}^{2x - 3} \\ {7}^{2x} = {7}^{6x - 9} \\ as \: the \: bases \: are \: equal \\ we \: equate \: exponents \\ \\ 2x = 6x - 9 \\ 9 = 6x - 2x \\ 6x - 2x = 9 \\ 4x = 9 \\ x = \frac{9}{4}$

Answer 2

Question :-

Find the value of x in the given expression.

$\sf{ {49}^{(x)} = {343}^{(2x - 3)} }$

Solution :-

$\sf\dashrightarrow {7}^{2x} = {7}^{3(2x - 3)}$

According to the exponent rule, same bases from both sides cancels out.

$\sf\dashrightarrow 2x = 3(2x - 3)$

$\sf\dashrightarrow 2x = (3 \times 2x) - (3 \times 3)$

$\sf\dashrightarrow 2x = (6x) - (9)$

$\sf\dashrightarrow 2x = 6x - 9$

$\sf\dashrightarrow 2x - 6x = - 9$

$\sf\dashrightarrow - 4x = - 9$

$\sf\dashrightarrow 4x = 9$

$\sf\dashrightarrow x = 9 \div 4$

$\dashrightarrow \boxed{\sf{ x = 2.25}}$

Therefore, Value Of x = 2.25