Question

Without using log, Solve for x. D" id="TexFormula1" title="27^{1-x} =\frac{1}{9^{2x} }" alt="27^{1-x} =\frac{1}{9^{2x} }" align="absmiddle" class="latex-formula">

Answer 1

ANSWER

$x = - 3$

EXPLANATION

The given equation is

$27^{1-x} =\frac{1}{9^{2x} }$

Recall that

$\frac{1}{ {a}^{m} } = {a}^{ - m}$

Apply this rule on the right hand side to get,

$27^{1-x} =9^{ - 2x}$

Express both sides to base 3.

$3^{3(1-x)} =3^{2( - 2x)}$

Equate the exponents:

3(1-x)=2(-2x)

Expand:

$3 - 3x = - 4x$

Group like terms,

$4x - 3x = - 3$

$x = - 3$