Math Problem Statement
If log10(x) = -2, what is the value of x?
Solution
The given problem is asking to solve for in the equation:
Step-by-step Solution:
-
The definition of logarithms states that if , then .
- In this case, , , and .
- So, we can rewrite the equation as:
-
Calculate :
Thus, the value of is:
Conclusion:
The correct answer is the first option:
Would you like more details on logarithmic functions or have any other questions?
Here are 5 related questions to expand on this topic:
- What is the logarithmic rule for converting logs to exponents?
- How do you solve logarithmic equations with different bases?
- What is the inverse function of a logarithmic equation?
- How would you handle a logarithmic equation with a variable in the base?
- What happens if the logarithmic equation is ?
Tip: Logarithms are just another way to express powers! For example, is the same as saying .
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponential Functions
Formulas
log_b(a) = c implies a = b^c
x = 10^-2
Theorems
Properties of Logarithms
Suitable Grade Level
Grades 9-12