Math Problem Statement

Solve the equation.

log(x) = 4

x = 

Solution

To solve the equation:

log(x)=4\log(x) = 4

we need to rewrite this in exponential form. The equation log(x)=4\log(x) = 4 means:

x=104x = 10^4

Now, calculating 10410^4:

x=10000x = 10000

So, the solution is:

x=10000x = 10000

Would you like further explanation on logarithmic transformations?

Here are some related questions to explore:

  1. What if log(x)=5\log(x) = 5? What would xx be?
  2. How would you solve ln(x)=4\ln(x) = 4 instead of log(x)=4\log(x) = 4?
  3. What are some real-world applications of logarithmic equations?
  4. How does changing the base of the logarithm affect the solution?
  5. How would you solve an equation like log(x)+2=5\log(x) + 2 = 5?

Tip: Remember that log(x)\log(x) typically implies base 10 if no base is specified, while ln(x)\ln(x) implies base ee.

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Math Problem Analysis

Mathematical Concepts

Algebra
Logarithmic Equations
Exponential Functions

Formulas

log(x) = y implies x = 10^y

Theorems

Definition of Logarithmic and Exponential Relationship

Suitable Grade Level

Grades 9-12