Math Problem Statement

Solve for x log(3x-2)=-1.2

Solution

We are given the equation:

log(3x2)=1.2\log(3x - 2) = -1.2

Steps to solve for xx:

  1. Exponentiate both sides: The logarithmic equation can be rewritten as an exponential equation. Since we have a base-10 logarithm (common logarithm), we can use the fact that:

    10log(y)=y10^{\log(y)} = y

    Applying this to both sides:

    3x2=101.23x - 2 = 10^{-1.2}

  2. Evaluate 101.210^{-1.2}: Calculate 101.210^{-1.2}:

    101.20.063110^{-1.2} \approx 0.0631

    So the equation becomes:

    3x2=0.06313x - 2 = 0.0631

  3. Solve for xx: Now, isolate xx by adding 2 to both sides:

    3x=2+0.06313x = 2 + 0.0631

    3x=2.06313x = 2.0631

    Divide by 3:

    x=2.063130.6877x = \frac{2.0631}{3} \approx 0.6877

Thus, the solution is approximately:

x0.6877x \approx 0.6877

Would you like more details or have any questions?

Here are 5 related questions:

  1. How do you convert a logarithmic equation into an exponential equation?
  2. What is the difference between natural logarithms and common logarithms?
  3. Can you solve log(2x+1)=0.5\log(2x + 1) = -0.5?
  4. What are the properties of logarithms that help simplify equations?
  5. What happens if the logarithmic argument inside becomes negative?

Tip: When solving logarithmic equations, always ensure the argument inside the logarithm remains positive, as logarithms of negative numbers are undefined in the real number system.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponential Equations

Formulas

Exponential equation from logarithm: 10^log(y) = y

Theorems

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Suitable Grade Level

Grades 10-12