Math Problem Statement
Solve for x: 5^x = 26. You may enter the exact value or round to 4 decimal places.
Solution
To solve the equation , we can use logarithms:
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Take the natural logarithm (ln) of both sides:
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Apply the logarithmic rule :
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Solve for :
Now, calculate the value using a calculator:
Thus, the solution is:
Would you like a more detailed explanation of logarithms or related concepts?
Here are five follow-up questions to explore this topic further:
- How does the base of the logarithm affect the solution?
- Can we solve the same equation using a different base for the logarithm (e.g., base 10)?
- What is the significance of logarithms in exponential growth problems?
- How would the solution change if the equation were ?
- What practical applications involve solving exponential equations like this one?
Tip: When solving equations involving exponents, always remember logarithmic properties to simplify calculations efficiently.
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Math Problem Analysis
Mathematical Concepts
Exponents
Logarithms
Formulas
log(a^b) = b * log(a)
x = ln(y)/ln(a)
Theorems
Logarithmic properties
Suitable Grade Level
Grades 10-12