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Popular >

4^x-3*2^x-4<0

Solution

4^{x} - 3 \cdot 2^{x} - 4 < 0

Solution

x < 2

+1

Interval Notation

(- \infty, 2)

Solution steps

4^{x} - 3 \cdot 2^{x} - 4 < 0

Apply exponent rules

(2^{x})^{2} - 3 \cdot 2^{x} - 4 < 0

Let

u = 2^{x}

u^{2} - 3 u - 4 < 0

u^{2} - 3 u - 4 < 0 : - 1 < u < 4

- 1 < u < 4

Substitute back

u = 2^{x}

- 1 < 2^{x} < 4

If

a < u < b

then

a < u and u < b

- 1 < 2^{x} and 2^{x} < 4

- 1 < 2^{x} :

True for all

x

2^{x} < 4 : x < 2

Combine the intervals

True for all x and x < 2

Merge Overlapping Intervals

x < 2

Popular Examples

3 n + 7 - 7 n < - 5

simplify 0.3*(0.73)/(0.9+0.73)simplify

0.3 \cdot \frac{0.73}{0.9 + 0.73}

4 z^{2} - 9 z - 1 = 0

simplify 0.7418*(800)/(1.7418)simplify

0.7418 \cdot \frac{800}{1.7418}

∣ 15 - 6 y ∣ \leq 9

Frequently Asked Questions (FAQ)

What is 4^x-3*2^x-4<0 ?
The solution to 4^x-3*2^x-4<0 is x<2