Math Problem Statement
Solution
The equation in the image is:
Let's solve this step by step:
-
Start by isolating the logarithmic term:
-
Convert the logarithmic equation to its exponential form: The logarithm is typically base 10, so we write:
-
To simplify , we can use the property of exponents:
The fifth root of 100 is approximately:
Since the left-hand side of the original equation was 25, and approximately equals 2.511, the equation as written is not exactly true. There might be a typo in the original problem.
Would you like more details or clarifications on this?
Here are 5 related questions:
- How do you convert logarithmic equations to exponential form?
- What is the difference between common and natural logarithms?
- How do you solve logarithmic equations with different bases?
- What are the properties of logarithms that can help simplify calculations?
- How do fractional exponents relate to roots?
Tip: When solving logarithmic equations, always make sure you correctly identify the base of the logarithm, which is typically 10 (common logarithm) or (natural logarithm).
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Logarithms
Algebra
Exponential Equations
Formulas
log_b(x) = y implies b^y = x
logarithm properties: log(x^n) = n*log(x)
Theorems
Exponential and Logarithmic Relationship
Suitable Grade Level
Grades 10-12