Math Problem Statement
Solve for x log(3x-2)=-1.2
Solution
We are given the equation:
Steps to solve for :
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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:
Applying this to both sides:
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Evaluate : Calculate :
So the equation becomes:
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Solve for : Now, isolate by adding 2 to both sides:
Divide by 3:
Thus, the solution is approximately:
Would you like more details or have any questions?
Here are 5 related questions:
- How do you convert a logarithmic equation into an exponential equation?
- What is the difference between natural logarithms and common logarithms?
- Can you solve ?
- What are the properties of logarithms that help simplify equations?
- 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