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Popular >

2^x>-x+3

Solution

2^{x} > - x + 3

Solution

x > 1

+1

Interval Notation

(1, \infty)

Solution steps

2^{x} > - x + 3

Prepare

2^{x} > - x + 3

for Lambert form:

1 > (- x + 3) e^{- l n (2) x}

Rewrite the equation with

(- x + 3) ln (2) = u

and

x = - \frac{u - 3 ln ( 2 )}{ln ( 2 )}

1 > (- (- \frac{u - 3 ln ( 2 )}{ln ( 2 )}) + 3) e^{- l n (2) (- \frac{u - 3 l n ( 2 )}{l n ( 2 )})}

Simplify

1 > e^{u - 3 l n (2)} (\frac{u - 3 ln ( 2 )}{ln ( 2 )} + 3)

Rewrite

1 > e^{u - 3 l n (2)} (\frac{u - 3 ln ( 2 )}{ln ( 2 )} + 3)

in Lambert form:

e^{u} u < 8 ln (2)

Solve

e^{u} u < 8 ln (2) : u < 2 ln (2)

u < 2 ln (2)

Substitute back

(- x + 3) ln (2) = u,

solve for

x

Solve

(- x + 3) ln (2) < 2 ln (2) : x > 1

x > 1

Popular Examples

(2^n)/((2^{n+2)-3)}< 1/4

\frac{2 ^{n}}{( 2 ^{n + 2} - 3 )} < \frac{1}{4}

((4^x+2))/9 <2^{x-1}

\frac{( 4 ^{x} + 2 )}{9} < 2^{x - 1}

0. 3^{x} < 1 0^{- 4}

2^{n} - 2 \geq 4

solvefor x,f>4^x-2 solve for

x, f > 4^{x} - 2

Frequently Asked Questions (FAQ)

What is 2^x>-x+3 ?
The solution to 2^x>-x+3 is x>1