What is the value of log7 343?
Understand the Problem
The question is asking to find the value of the logarithm with base 7 of 343. This can be expressed mathematically as log7(343), and the solution involves determining what exponent, when 7 is raised to it, will equal 343.
Answer
3
Answer for screen readers
The value of $\log_7(343)$ is 3.
Steps to Solve
- Identify the logarithm equation
We need to express the logarithm in its exponential form. The equation is:
$$ \log_7(343) = x $$
This means we are looking for $x$ such that:
$$ 7^x = 343 $$
- Express 343 as a power of 7
Next, we need to break down 343 into a power of 7. We know that:
$$ 7^1 = 7 $$
$$ 7^2 = 49 $$
$$ 7^3 = 343 $$
Thus, we can express 343 as:
$$ 343 = 7^3 $$
- Set the exponents equal
Now that we have rewritten 343 as a power of 7, we substitute it into our original equation:
$$ 7^x = 7^3 $$
Since the bases are the same, we can set the exponents equal to each other:
$$ x = 3 $$
The value of $\log_7(343)$ is 3.
More Information
This logarithmic calculation tells us that 7 raised to the power of 3 equals 343. In real-world contexts, logarithms can represent growth processes, such as population growth or sound intensity.
Tips
- Incorrectly expressing the power: Some might confuse the powers of 7 and miscalculate. Always verify the power calculations.
- Ignoring base matching: When setting the exponents equal, ensure that the bases are actually the same.
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