Math Problem Statement
Solve: log 8x - log 2 = log 32
Solution
Let's solve the equation:
Step-by-step:
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Apply the logarithmic rule : This simplifies to:
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Since the logarithms are equal, we can drop the log and equate the inside of the logarithms:
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Solve for :
Thus, the solution is .
Answer: (This matches one of the choices in the image you uploaded).
Would you like further explanation or help with similar problems? Here's some related practice to deepen your understanding:
- How do you handle equations involving logarithms with different bases?
- What if the equation involved instead of subtraction?
- Can you explain the logarithmic identity ?
- How can you verify the solution to a logarithmic equation?
- What’s the domain of a logarithmic function?
Tip: Always remember to check that the argument of a logarithm is positive, as the logarithm of a non-positive number is undefined.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Logarithmic Equations
Properties of Logarithms
Formulas
log a - log b = log (a/b)
If log A = log B, then A = B
Theorems
Properties of Logarithms
Equality Property of Logarithms
Suitable Grade Level
Grades 9-12