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Popular >

34^x-52^{x+1}<= 8

Solution

3 \cdot 4^{x} - 5 \cdot 2^{x + 1} \leq 8

Solution

x \leq 2

+1

Interval Notation

(- \infty, 2]

Solution steps

3 \cdot 4^{x} - 5 \cdot 2^{x + 1} \leq 8

Apply exponent rules

3 (2^{x})^{2} - 5 \cdot 2^{x} \cdot 2 \leq 8

Let

u = 2^{x}

3 u^{2} - 5 u \cdot 2 \leq 8

3 u^{2} - 5 u \cdot 2 \leq 8 : - \frac{2}{3} \leq u \leq 4

- \frac{2}{3} \leq u \leq 4

Substitute back

u = 2^{x}

- \frac{2}{3} \leq 2^{x} \leq 4

If

a \leq u \leq b

then

a \leq u and u \leq b

- \frac{2}{3} \leq 2^{x} and 2^{x} \leq 4

- \frac{2}{3} \leq 2^{x} :

True for all

x

2^{x} \leq 4 : x \leq 2

Combine the intervals

True for all x and x \leq 2

Merge Overlapping Intervals

x \leq 2

Popular Examples

8 y - (2 y - 17) = 41

simplify 5n+6+(-7n)simplify

5 n + 6 + (- 7 n)

simplify 9-1/5 simplify

9 - \frac{1}{5}

5 x - 6 < 9

4 x = - 12

Frequently Asked Questions (FAQ)

What is 3*4^x-5*2^{x+1}<= 8 ?
The solution to 3*4^x-5*2^{x+1}<= 8 is x<= 2