5 Questions
Simplify $2^{3/2-4}$.
$2^{-3/2}$
Solve the equation: $2^{x} = rac{1}{16}$.
$x = -4$
Solve the equation: $log_{10}(x + 2) = 2.5$.
$x = 98$
Simplify $(rac{3L^{2}Q^{2}}{e^{2}})^{2}$.
$rac{9L^{4}Q^{4}}{e^{4}}$
Solve the equation: $2^{2x+1} = 7$.
$x = rac{1}{2}$
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
Solve algebraic expressions and equations involving indices, exponents, and logarithms. Test your skills in simplifying expressions and solving equations.
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