To solve this inequality, we can first rewrite it in exponential form:
0.5^(3-2x) > 4^1
Simplify the equation by converting the bases to the same value:
(0.5^3)(0.5^(-2x)) > 4
0.5^3 = 0.1254 = 2^2
0.125(0.5^(-2x)) > 2^2
0.125 * (1 / (0.5^2x)) > 4
0.125 / 0.25^x > 4
0.5^x > 32
Now we can rewrite the inequality in terms of logs:
x > log0.5 32
x > log 32 / log 0.5
x > 5
Therefore, the solution to the inequality is x > 5.
To solve this inequality, we can first rewrite it in exponential form:
0.5^(3-2x) > 4^1
Simplify the equation by converting the bases to the same value:
(0.5^3)(0.5^(-2x)) > 4
0.5^3 = 0.125
4 = 2^2
0.125(0.5^(-2x)) > 2^2
0.125 * (1 / (0.5^2x)) > 4
0.125 / 0.25^x > 4
0.5^x > 32
Now we can rewrite the inequality in terms of logs:
x > log0.5 32
x > log 32 / log 0.5
x > 5
Therefore, the solution to the inequality is x > 5.