If log 3=A and log 5=B express
Log 75 in terms of A and B. (using the Law of Exponents)
Well, well, well... it's time to put on the math clown shoes and tackle this question! Let's get started.
Since we know that log 3 = A and log 5 = B, we can use the laws of logarithms to express log 75 in terms of A and B.
First, let's take a step back and analyze the number 75. We can break it down into its prime factors, 3 and 5. Now, we can rewrite 75 as 3^1 * 5^2.
Applying the law of exponents, we can rewrite this as (3^1) * (5^2), which is equal to 3 * (5^2).
Now, here comes the hilarious part! We'll use the sum law of logarithms to express log 75:
log 75 = log (3 * (5^2))
Using the sum law, we can split this up into:
log 75 = log 3 + log (5^2)
Substituting A and B for log 3 and log 5 respectively, we have:
log 75 = A + 2B
And there you have it! We've expressed log 75 in terms of A and B using the law of exponents. Hope that brought a smile to your face!
To express log 75 in terms of A and B, we will use the properties of logarithms, particularly the laws of exponents.
We know that log 3 = A and log 5 = B.
First, let's express 75 as the product of prime numbers:
75 = 3 × 5 × 5
Now, we can use the law of exponents for logarithms, specifically:
log (x × y) = log(x) + log(y)
Applying this law to 75, we get:
log 75 = log (3 × 5 × 5) = log 3 + log 5 + log 5
Since log 3 = A and log 5 = B, we can substitute these values into the equation:
log 75 = A + B + B
Combining like terms, we get:
log 75 = A + 2B
Therefore, log 75 can be expressed in terms of A and B as A + 2B.
To express log 75 in terms of A and B using the Law of Exponents, we need to manipulate the given logarithmic expressions.
First, let's look at the number 75 and see if we can find relationships with 3 and 5.
We can express 75 as a product of powers of 3 and 5:
75 = 3^1 * 5^2
By using the Law of Exponents, we know that the logarithm of a product is the sum of the logarithms of the individual factors. Therefore, we can write:
log 75 = log (3^1 * 5^2)
Now, applying the Law of Exponents for logarithms, we can rewrite this expression as:
log 75 = log 3^1 + log 5^2
Since log 3 is equal to A and log 5 is equal to B (as given), we can substitute these values:
log 75 = A + 2B
Hence, log 75 can be expressed in terms of A and B as A + 2B.
75=3*5^2
log75=log3+ 2log5