Zurtex said:
You sure you have read the edits?primarygun said:
What's edited?
The original question.primarygun said:
To solve this problem, we can use the change of base formula, which states that log(basea)b = logc(b)/logc(a). In this case, we want to find log(base5)36, so we can use either log2 or log3 as our base. Let's use log2 for this example. We can rewrite the problem as log2(36)/log2(5). Using a calculator, we can find that log2(36) = 5.1699 and log2(5) = 2.3219. Therefore, log(base5)36 ≈ 5.1699/2.3219 ≈ 2.2302.
Yes, it is possible to solve this problem without a calculator. You can use the logarithm identities, such as log(ab) = log(a) + log(b), to rewrite the problem as log(6^2)/log(5), which equals 2log(6)/log(5). Then, you can use the change of base formula to find log(6)/log(5) ≈ 1.5849, and finally, multiply by 2 to get 2log(6)/log(5) ≈ 3.1699.
To check your answer, you can use a calculator to evaluate log2(36)/log2(5) and log3(36)/log3(5). Both of these expressions should give you the same result, which is approximately 2.2302. You can also plug this value back into the original equation log(base5)36 and see if it equals to 36.
Yes, you can use any other base as long as you are consistent in your calculations. However, using log2 or log3 is most convenient since they are easy to evaluate on a calculator.
Logarithms are useful because they allow us to solve for unknown variables that are in exponents. In this case, log(base5)36 tells us what exponent we need to raise 5 to in order to get 36. By using logarithms, we can easily find the value of this exponent without having to use trial and error or a lengthy calculation.
