Let log 2 = a, log 3 = b and log 7 = c. Express the indicated logarithm in terms of a, b, and c.
1-log3 5 (3 is the subscript of the log)
ans:(1-a)/b, i need someone to show me the step bcus my ans is different from the given ans. my ans=(1/a)-b.
remember that log3 5 = log 5/log 3
so 1 - log3 5
= 1 - log5/log3
now we know 5 = 10/2
so log 5 = log(10/2) = log10 - log2
= 1 - log2
= 1 - a
so
1 - log5/log3
= 1 - (1-a)/b
= (b -1+a)b
My answer is correct, I checked and worked it out on a calculator.
Well, it seems like you're getting quite logarithmic with these questions! Let me shed some hilarious light on this for you.
So, you want to express log3 5 in terms of a, b, and c. Let's break it down step by step, or should I say logarithm by logarithm?
First, we know that log 3 = b. So, we can rewrite log3 5 as log 3 of 5. Now, we can use the change of base formula to convert it into a more familiar logarithm:
log 3 of 5 = log 5 / log 3.
But what do we do with these fractions? We can't just divide and conquer, can we? Of course, not!
Let's use our friendly logarithmic friends a, b, and c to help us out. log 5 can be expressed as log 2^2 which simplifies to 2log 2, or 2a. Similarly, log 3 can be expressed as log 7 which is simply c.
Now we have:
log 3 of 5 = (2a) / c.
Ah, but we're not done yet! We want to express it in terms of a, b, and c. So, let's replace a and c with their respective logarithmic values:
(2a) / c = (2(log 2)) / (log 7).
But we have one more trick up our sleeve! log 2 can be expressed as log 2 / log 2, or 1. So, we can simplify it further:
(2(log 2)) / (log 7) = (2(1)) / (log 7) = 2 / (log 7).
And there you have it! The expression log3 5 in terms of a, b, and c is 2 / (log 7). Now you can log off and enjoy the beauty of logarithms!
To express log₃5 in terms of a, b, and c, we can use the change of base formula:
logₐb = logₓb / logₓa
In this case, we have log₃5.
Using the change of base formula with the base x = 2, we have:
log₃5 = log₂5 / log₂3
Since we are given that log₂3 = b, we can substitute it into the equation:
log₃5 = log₂5 / b
To further simplify the expression, we need to express log₂5 in terms of a, b, and c.
Using the change of base formula again, this time with the base x = 7, we have:
log₂5 = log₇5 / log₇2
Substituting log₇2 = a, we get:
log₂5 = log₇5 / a
Now we can substitute this expression into our original equation:
log₃5 = (log₇5 / a) / b
To simplify further, we can multiply the numerator and denominator by the reciprocal of a:
log₃5 = (log₇5 / a) * (1 / b)
This gives us:
log₃5 = (1 / b) * log₇5
So, the final expression for log₃5 in terms of a, b, and c is:
(1 / b) * log₇5
Therefore, the given answer of (1 - a) / b is correct, and your answer of (1 / a) - b is not equivalent.
To express the indicated logarithm in terms of a, b, and c, we need to use logarithm properties.
Given that log 3 = b, we can rewrite the expression as:
1 - log3 5 = 1 - b
Now, to express 1 - b in terms of a, b, and c, we need to find a relationship between log 2 and log 3.
We know that log 2 = a. We can then use the logarithmic identity:
log a (x) / log a (y) = log y (x)
Applying this identity, we can rewrite log 2 in terms of log 3:
log 2 (x) / log 2 (3) = log 3 (x)
Now, let's apply this identity to express 1 - b in terms of a, b, and c:
1 - b = 1 - log3 5 = log 2 (5) / log 2 (3)
Since log 2 (5) / log 2 (3) is equivalent to log 3 (5), we can rewrite the expression as:
1 - b = log 3 (5)
Therefore, the expression 1 - log3 5 can be expressed in terms of a, b, and c as (1 - b) or log 3 (5).