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Popular >

x+3^x<4

Solution

x + 3^{x} < 4

Solution

x < 1

+1

Interval Notation

(- \infty, 1)

Solution steps

x + 3^{x} < 4

Subtract

x

from both sides

x + 3^{x} - x < 4 - x

Simplify

3^{x} < 4 - x

Prepare

3^{x} < 4 - x

for Lambert form:

1 < (4 - x) e^{- l n (3) x}

Rewrite the equation with

(- x + 4) ln (3) = u

and

x = - \frac{u - 4 ln ( 3 )}{ln ( 3 )}

1 < (4 - (- \frac{u - 4 ln ( 3 )}{ln ( 3 )})) e^{- l n (3) (- \frac{u - 4 l n ( 3 )}{l n ( 3 )})}

Simplify

1 < e^{u - 4 l n (3)} (4 + \frac{u - 4 ln ( 3 )}{ln ( 3 )})

Rewrite

1 < e^{u - 4 l n (3)} (4 + \frac{u - 4 ln ( 3 )}{ln ( 3 )})

in Lambert form:

e^{u} u > 81 ln (3)

Solve

e^{u} u > 81 ln (3) : u > 3 ln (3)

u > 3 ln (3)

Substitute back

(- x + 4) ln (3) = u,

solve for

x

Solve

(- x + 4) ln (3) > 3 ln (3) : x < 1

x < 1

Popular Examples

\frac{1}{5} x^{2} - 5 = 0

longsub 1-0.15 long subtraction

1 - 0.15

simplify (3+2/3)/(4+2/3)simplify

\frac{3 + \frac{2}{3}}{4 + \frac{2}{3}}

3x+1>10\lor 3-4x>19

3 x + 1 > 10 or 3 - 4 x > 19

\frac{9 - x}{- 2} \geq - 6

Frequently Asked Questions (FAQ)

What is x+3^x<4 ?
The solution to x+3^x<4 is x<1