How do you solve the exponential inequality $8^(x-1)<=32^(3x-2)$ ?

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Answer 1 · 2018-06-19T07:28:57

$x>=3/4$

$8^(x-1)<=32^(3x-2)$

change the $8 " and "32$ to powers of 2

$(2^3)^(x-1)<=(2^5)^(3x-2)$

ie

$2^(3x-1)<=2^(15x-10)$

$=>3x-1<=15x-10$

solve for $x$

$-1+10<=15x-3x$

$9<=12x$

$12x>=9$

$=>x>=9/12$

$x>=3/4$

How do you solve the exponential inequality 8^(x-1)<=32^(3x-2)8^(x-1)<=32^(3x-2)?