en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2^{x+3}<= 9^{3x}

Solution

2^{x + 3} \leq 9^{3 x}

Solution

x \geq \frac{3 ln ( 2 )}{- ln ( 2 ) + 6 ln ( 3 )}

+2

Interval Notation

[\frac{3 ln ( 2 )}{- ln ( 2 ) + 6 ln ( 3 )}, \infty)

Decimal Notation

x \geq 0.35253 \dots

Solution steps

2^{x + 3} \leq 9^{3 x}

If

f (x) \leq g (x)

then

ln (f (x)) \leq ln (g (x))

ln (2^{x + 3}) \leq ln (9^{3 x})

Simplify

ln (2^{x + 3}) : ln (2) (x + 3)

Simplify

ln (9^{3 x}) : 2 ln (3) \cdot 3 x

ln (2) (x + 3) \leq 2 ln (3) \cdot 3 x

ln (2) (x + 3) \leq 2 ln (3) \cdot 3 x : x \geq \frac{3 ln ( 2 )}{- ln ( 2 ) + 6 ln ( 3 )}

x \geq \frac{3 ln ( 2 )}{- ln ( 2 ) + 6 ln ( 3 )}

Popular Examples

simplify 5sqrt(2)*5sqrt(2)simplify

52 \cdot 52

simplify (a^{-3}b^4)/(a^{-5)b^5}simplify

\frac{a ^{- 3} b ^{4}}{a ^{- 5} b ^{5}}

\frac{2 x - 5}{x - 2} < 1

simplify 5^4 simplify

5^{4}

x^{2} - 2 x + 80 = 0

Frequently Asked Questions (FAQ)

What is 2^{x+3}<= 9^{3x} ?
The solution to 2^{x+3}<= 9^{3x} is x>= (3ln(2))/(-ln(2)+6ln(3))