Math Problem Statement

Find the exact solutions of various equations involving exponentials, logarithms, and algebraic expressions.

Solution

It looks like you've uploaded a math problem sheet. This sheet contains various equations that need to be solved, covering topics such as exponential equations, logarithms, and algebraic manipulations.

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Math Problem Analysis

Mathematical Concepts

Exponential Equations
Logarithmic Equations
Algebraic Manipulation
Quadratic Equations

Formulas

Quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a
Laws of exponents: a^m * a^n = a^(m+n), (a^m)^n = a^(m*n)
Logarithmic properties: log_a(xy) = log_a(x) + log_a(y), log_a(x/y) = log_a(x) - log_a(y)

Theorems

Exponent Rules
Logarithm Properties
Quadratic Formula Theorem

Suitable Grade Level

Grades 9-12