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Popular >

(e^x-2)(e^x-3)<= 2e^x

Solution

(e^{x} - 2) (e^{x} - 3) \leq 2 e^{x}

Solution

0 \leq x \leq ln (6)

+2

Interval Notation

[0, ln (6)]

Decimal Notation

0 \leq x \leq 1.79175 \dots

Solution steps

(e^{x} - 2) (e^{x} - 3) \leq 2 e^{x}

Let

u = e^{x}

(u - 2) (u - 3) \leq 2 u

(u - 2) (u - 3) \leq 2 u : 1 \leq u \leq 6

1 \leq u \leq 6

Substitute back

u = e^{x}

1 \leq e^{x} \leq 6

If

a \leq u \leq b

then

a \leq u and u \leq b

1 \leq e^{x} and e^{x} \leq 6

1 \leq e^{x} : x \geq 0

e^{x} \leq 6 : x \leq ln (6)

Combine the intervals

x \geq 0 and x \leq ln (6)

Merge Overlapping Intervals

0 \leq x \leq ln (6)

Popular Examples

(11x)/5-4/5 = 1/5

\frac{11 x}{5} - \frac{4}{5} = \frac{1}{5}

f = 4 (0) + 3

simplify 3/(sqrt(10))simplify

\frac{3}{10}

simplify 1/(x-y)+(2x-y)/(x^2-y^2)simplify

\frac{1}{x - y} + \frac{2 x - y}{x ^{2} - y ^{2}}

simplify 3/5-3/4 simplify

\frac{3}{5} - \frac{3}{4}

Frequently Asked Questions (FAQ)

What is (e^x-2)(e^x-3)<= 2e^x ?
The solution to (e^x-2)(e^x-3)<= 2e^x is 0<= x<= ln(6)