Question

8^(x-2)*(1/2)^(4-3x)=(0.062
5)^x

Answer 1

Answer :


${8}^{x - 2} \times ( \frac{1}{2} ) {}^{4 - 3x} = (0.0625) {}^{x} \\ \\ write \: the \: expression \: in \: the \: exponential \: form \: with \: base \: 2 \\ \\ 2 {}^{3x - 6} \times ( \frac{1}{4} {)}^{4 - 3x} = 2 {}^{ - 4x} \\ \\ express \: with \: positive \: exponent \: by \: using \\ ( \frac{1}{a} ) {}^{ - n} = {a}^{n}$
$= > \: 2 {}^{3x - 6} \times {2}^{ - 4 + 3x} = {2}^{ - 4x} \\ \\ calculate \: the \: product \\ \\ {2}^{6x - 10} = {2}^{ - 4x} \\ \\ since \: bases \: are \: same \: \\ set \: the \: exponents \: equal \\ \\ 6x - 10 = - 4x \\ \\ 6x + 4x = 10 \\ \\ 10x = 10 \\ \\ x = \frac{10}{10} \\ \\ x = 1$


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