Question

find the value of x when

Answer 1

Answer -

$((( \frac{3}{7} {)}^{4} {)}^{2} {)}^{x + 2} = ( \frac{3}{7} {)}^{x + 5} \div ( \frac{3}{7} {)}^{ - 2x - 6} \\ \\ simplify \: by \: multiplying \: the \: exponents \\ \\ (( \frac{3}{7} {)}^{8} {)}^{x + 2} = ( \frac{3}{7} {)}^{3x + 11} \\ \\ ( \frac{3}{7} {)}^{8x + 16} = ( \frac{3}{7} {)}^{3x + 11} \\ \\since \: the \: bases \: are \: same \: so \: set \: the \: exponents \: equal$

$8x + 16 = 3x + 11 \\ \\ 8x - 3x = 11 - 16 \\ \\ 5x = - 5 \\ \\ x = \frac{ - 5}{5} \\ \\ x = - 1$


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