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Popular >

3^x<27*3^{-x}

Solution

3^{x} < 27 \cdot 3^{- x}

Solution

x < \frac{3}{2}

+2

Interval Notation

(- \infty, \frac{3}{2})

Decimal Notation

x < 1.5

Solution steps

3^{x} < 27 \cdot 3^{- x}

Apply exponent rules

3^{x} < 27 \cdot \frac{1}{3 ^{x}}

If

f (x) > 0

we can multiply or devide both sides of inequality by

f (x)

3^{x}

is greater than

0

for all

x

3^{x} \cdot 3^{x} < 27 \cdot \frac{1}{3 ^{x}} \cdot 3^{x}

Simplify

3^{2 x} < 27

Apply exponent rules

2 x < 3

Divide both sides by

2

x < \frac{3}{2}

Popular Examples

3^{t} - 4 t - 1 < 0

3^{1/((x+1))}>9

3^{\frac{1}{( x + 1 )}} > 9

2^{x} + x - 3 < 0

2^{x} > - x + 3

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

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

Frequently Asked Questions (FAQ)

What is 3^x<27*3^{-x} ?
The solution to 3^x<27*3^{-x} is x< 3/2