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Popular >

(2^x-3)(2^x-5)<= 15

Solution

(2^{x} - 3) (2^{x} - 5) \leq 15

Solution

x \leq 3

+1

Interval Notation

(- \infty, 3]

Solution steps

(2^{x} - 3) (2^{x} - 5) \leq 15

Let

u = 2^{x}

(u - 3) (u - 5) \leq 15

(u - 3) (u - 5) \leq 15 : 0 \leq u \leq 8

0 \leq u \leq 8

Substitute back

u = 2^{x}

0 \leq 2^{x} \leq 8

If

a \leq u \leq b

then

a \leq u and u \leq b

0 \leq 2^{x} and 2^{x} \leq 8

0 \leq 2^{x} :

True for all

x

2^{x} \leq 8 : x \leq 3

Combine the intervals

True for all x and x \leq 3

Merge Overlapping Intervals

x \leq 3

Popular Examples

(3^{x})^{2} < 81

(3^{x/2})^{x-1}>= (3/9)^{x-3}

(3^{\frac{x}{2}})^{x - 1} \geq (\frac{3}{9})^{x - 3}

3^{x} \geq 5

(((3^x-5^x)(x-2)))/((x^2+5x+2))>= 0

\frac{( ( 3 ^{x} - 5 ^{x} ) ( x - 2 ) )}{( x ^{2} + 5 x + 2 )} \geq 0

log_{x}(((4x+5))/((6-5x)))<-1

lo g_{x} (\frac{( 4 x + 5 )}{( 6 - 5 x )}) < - 1

Frequently Asked Questions (FAQ)

What is (2^x-3)(2^x-5)<= 15 ?
The solution to (2^x-3)(2^x-5)<= 15 is x<= 3