Math Problem Statement

If log10(x) = -2, what is the value of x?

Solution

The given problem is asking to solve for xx in the equation:

log10x=2\log_{10} x = -2

Step-by-step Solution:

  1. The definition of logarithms states that if logba=c\log_b a = c, then a=bca = b^c.

    • In this case, b=10b = 10, c=2c = -2, and a=xa = x.
    • So, we can rewrite the equation as: x=102x = 10^{-2}
  2. Calculate 10210^{-2}: 102=110010^{-2} = \frac{1}{100}

Thus, the value of xx is:

x=1100x = \frac{1}{100}

Conclusion:

The correct answer is the first option: x=1100x = \frac{1}{100}

Would you like more details on logarithmic functions or have any other questions?

Here are 5 related questions to expand on this topic:

  1. What is the logarithmic rule for converting logs to exponents?
  2. How do you solve logarithmic equations with different bases?
  3. What is the inverse function of a logarithmic equation?
  4. How would you handle a logarithmic equation with a variable in the base?
  5. What happens if the logarithmic equation is logbx=1\log_b x = -1?

Tip: Logarithms are just another way to express powers! For example, logbx=y\log_b x = y is the same as saying x=byx = b^y.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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