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# Algebra and Indices Quiz

Created by
@MatchlessRiemann

### 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 $(rac{3L^{2}Q^{2}}{e^{2}})^{2}$.

<p>$rac{9L^{4}Q^{4}}{e^{4}}$</p> Signup and view all the answers

### Solve the equation: $2^{2x+1} = 7$.

<p>$x = rac{1}{2}$</p> 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

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## Description

Solve algebraic expressions and equations involving indices, exponents, and logarithms. Test your skills in simplifying expressions and solving equations.

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