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Popular >

10^n>2^{2022}

Solution

1 0^{n} > 2^{2022}

Solution

n > \frac{2022 ln ( 2 )}{ln ( 10 )}

+2

Interval Notation

(\frac{2022 ln ( 2 )}{ln ( 10 )}, \infty)

Decimal Notation

n > 608.68265 \dots

Solution steps

1 0^{n} > 2^{2022}

If

f (x) > g (x)

then

ln (f (x)) > ln (g (x))

ln (1 0^{n}) > ln (2^{2022})

Simplify

ln (1 0^{n}) : ln (10) n

Simplify

ln (2^{2022}) : 2022 ln (2)

ln (10) n > 2022 ln (2)

Divide both sides by

ln (10)

n > \frac{2022 ln ( 2 )}{ln ( 10 )}

Popular Examples

e^{x} > - 2

(3/5)^x>= 127/25

(\frac{3}{5})^{x} \geq \frac{127}{25}

3^{x + 1} - 1 \geq 0

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

2 (5)^{x} > 250

Frequently Asked Questions (FAQ)

What is 10^n>2^{2022} ?
The solution to 10^n>2^{2022} is n>(2022ln(2))/(ln(10))