Question 944474
{{{ (0.25)^x = 16}}}
using logs
{{{log((0.25)^x) = log(16)}}}
log equiv of exponents
{{{x*log((0.25)) = log(16)}}}
x = {{{log(16)/log(.25)}}}
x = -2
:
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From your comment
solve: 16x^-3 = 2x^-6
The reciprocal gets rid of the neg exponents
{{{16/x^3}}} = {{{2/x^6}}}
cross multiply
16x^6 = 2x^3
divide both sides by 2
8x^6 = x^3
divide both sides by x^3
8x^3 = 1
divide both sides by 8
x^3 = {{{1/8}}}
find the cube root of both sides
x = {{{3sqrt(1/8)}}}
x = {{{1/2}}}