3-ln(2x)<2 — step-by-step solution

⚠Ⓘ 2x is read as the product 2*x: for a power, write 2^x

1) Let's solve in

ℝ

3 - \ln (2 x) < 2

3 - \ln (2 x) - 2 < 0

1 - \ln (2 x) < 0

-1

is negative, you must reverse the inequality sign when dividing/multiplying by this term

Divide both sides by

-1

Let's apply the exp function on both sides:

e^{\ln (2 x)} > e^{1}

2 x > e

Solution obtained:

x > \frac{e}{2}

2) Let's solve for x:

2 x > 0

using

x > \frac{e}{2}

The expression can be simplified by:

2

Solution found:

x > 0

Let's aggregate the different solutions to find the overall solution:

▶Solution obtained:

x \in (\frac{e}{2}, +∞)

3) The numeric value of:

x \in (\frac{e}{2}, +∞)

is:

x \in (\frac{\approx 2.7183}{2}, +∞)

▷

x \in (\approx 1.3591, +∞)