Question

$\frac{16}{25} \times \frac{64}{5} = ( \frac{4}{5} ) {}^{2x + 4} \: \: \: \: \: \: \: \: find \: x$
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Answer 1

${\bigstar}$SOLUTION${\bigstar}$

➠$\frac{16}{25} \times \frac{64}{5} = { ( \frac{4}{5} )}^{2x + 4}$

➠$\frac{ {4}^{2} }{ {5}^{2} } \times \frac{ {4}^{3} }{5} = {( \frac{4}{5} )}^{2x + 4}$

➠$\frac{ {4}^{2 + 3} }{ {5}^{2 + 1} } = \frac{ {4}^{2x + 4} }{ {5}^{2x + 4} }$

➠$\frac{ {4}^{5} }{ {5}^{3} } = \frac{ {4}^{2x + 4} }{ {5}^{2x + 4} }$

As the bases are same ,equate the powers of numerators and denominators separately.

NUMERATOR:

➠5 = 2x + 4

➠2x = 5-4

➠x = 1/2

DENOMINATOR:

➠3 = 2x + 4

➠2x = 3-4

➠x = -1/2