Solving Exponential Equations with Logs
Read this topicExplanations 3
- (Video) Solving Exponential Equations With Different Bases Using Logarithms - Algebra by The Organic Chemistry Tutor Check out this video by The Organic Chemistry Tutor to learn…
By Trisha, Anusha Rahman
- Turns out, we can use logs to solve exponential equations! Let's look at an example. 25x+3=63x−42^{5x+3} = 6^{3x-4}25x+3=63x−4 We can solve this equation using logs! We can star…
By Trisha, Anusha Rahman
- Solving Exponential Equations with Logs Sometimes, exponential equations can't be solved just by making the bases match. That’s when we use logarithms to help! Many exponential …
By Trisha, Anusha Rahman
Problems 11
- The inequality e2x−2ex+1≤0e^{2x} - 2e^x + 1 \le 0e2x−2ex+1≤0 is satisfied for values of xxx in an interval [a,b][a,b][a,b]. Find b−ab-ab−a.
- What integer value of xxx satisfies the following equation? ∣3x−25∣<5|3^x - 25| < 5∣3x−25∣<5
- For which values of xxx is the following inequality true? 2x+1≥4x2^{x+1} \ge 4^x2x+1≥4x
- What values of xxx satisfy the following inequality? 32x+1>34x3^{2x+1} > 3^{4x}32x+1>34x
- What values of xxx satisfy the following inequality? (12)2x>(12)x+4\left(\frac{1}{2}\right)^{2x}>\left(\frac{1}{2}\right)^{x+4}(21)2x>(21)x+4
- What values of xxx satisfy the inequality? 4x−1<83x4^{x-1} < 8^{3x}4x−1<83x
- What values of xxx satisfy the inequality? 32x−9>9−x+13^{2x-9} > 9^{-x+1}32x−9>9−x+1
- What values of xxx satisfy this inequality? 25x>58−5x2^{5x} > 5^{8-5x}25x>58−5x
- What values of xxx satisfy this inequality? 2x+4x>62^{x} +4^{x} > 62x+4x>6
- What values of xxx satisfy the following inequality? 53x+1>5−x+55^{3x+1} > 5^{-x+5}53x+1>5−x+5
- What values of xxx satisfy the following inequality? (23)x>(23)−x+4\left(\frac {2}{3}\right)^{x} > \left(\frac{2}{3}\right)^{-x+4}(32)x>(32)−x+4