Podcast
Questions and Answers
Simplify $\frac{15^{2}e^{2}}{e^{2}}$.
Simplify $\frac{15^{2}e^{2}}{e^{2}}$.
$15^{2}$
Solve for $x$: $5^{x+3} imes 5^{x} = 5^{4}$.
Solve for $x$: $5^{x+3} imes 5^{x} = 5^{4}$.
$x = -2$
What is the estimated population of the village in 1990, given it was 753 in 1980 with a specific growth model?
What is the estimated population of the village in 1990, given it was 753 in 1980 with a specific growth model?
Approximately 906
Solve for $K$: $(1+K)^{0.5} = 2$.
Solve for $K$: $(1+K)^{0.5} = 2$.
Signup and view all the answers
Solve for $x$: $log_{10}(x + 2) = 2.5$.
Solve for $x$: $log_{10}(x + 2) = 2.5$.
Signup and view all the answers
Study Notes
Simplifying Expressions
- Simplify expressions by rewriting them with positive indices only
- Examples of expressions to simplify:
- 2^(3/2-4)
- Q^(1.5)P
- √(8/(3^13+4))
- (15^2e^2)/e^2
- (3L^2Q^2/e^2)^2
- (3e^(0.1)/e)^2
Solving Equations
- Solve exponential equations:
- 2^x = 1/16
- 5^(x+3)5^x = 5^4
- 2^p3^Q = 1/3
- (1+K)^(0.5) = 2
- e^(2x+2)/e^2 = 2
- Solve logarithmic equations:
- log10(x + 2) = 2.5
- 2ln(x) - ln(x + 1) = 0
- 2^(2x+1) = 7
- e^(x+1) = 1.5
- 20 + (2.4)^x^2 = 32.5
Population Growth
- Population growth equation: P =
- Estimate population in:
- 1990
- 2000
- Find the year when the population reaches 1750 persons
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Simplify exponential expressions and solve equations involving exponents and logarithms, including solving for variables and evaluating numerical expressions.
