Math Problem Statement

give me a questions about solving each equation for x logarition

Solution

Here are some questions to practice solving for xx in logarithmic equations:

  1. Basic Logarithmic Equation:
    Solve for xx: log(x)=2\log(x) = 2

  2. Equation with a Base Other Than 10:
    Solve for xx: log2(x)=5\log_2(x) = 5

  3. Logarithmic Equation with Addition:
    Solve for xx: log(x+1)=3\log(x + 1) = 3

  4. Logarithmic Equation with Subtraction Inside the Argument:
    Solve for xx: log(x3)=2\log(x - 3) = 2

  5. Complex Logarithmic Equation Involving Multiple Terms:
    Solve for xx: log(x)+log(x+4)=2\log(x) + \log(x + 4) = 2

Tip:

When solving logarithmic equations, remember that rewriting the equation in exponential form often simplifies the solution process.

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Math Problem Analysis

Mathematical Concepts

Logarithmic Equations
Solving for Variables
Properties of Logarithms

Formulas

Logarithmic form: log_b(x) = y ⇔ b^y = x
Properties of logs: log_b(x) + log_b(y) = log_b(xy), log_b(x) - log_b(y) = log_b(x/y)

Theorems

Change of Base Theorem
Logarithmic Properties

Suitable Grade Level

Grades 9-12