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If log15 5 = x, what is the value of log15 243 in terms of x?
- a)3x
- b)3 - 3x
- c)3x - 5
- d)5 - 5 x
Correct answer is option 'D'. Can you explain this answer?
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If log155 = x, what is the value of log15 243 in terms of x?a)3xb)3 - ...
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If log155 = x, what is the value of log15 243 in terms of x?a)3xb)3 - ...
To find the value of log15 243 in terms of x, we need to express 243 as a power of 15.
Let's start by expressing 243 as a product of powers of prime numbers:
243 = 3 × 3 × 3 × 3 × 3 = 3^5
Now, let's express 15 as a power of a prime number:
15 = 3 × 5
So, we can write 243 as a power of 15:
243 = (3^5) = (3 × 3 × 3 × 3 × 3) = (3^2) × (3^3) = (3^2) × (3 × 3 × 3) = (3^2) × (3^1 × 3^1 × 3^1) = (3^2) × (3^1)^3 = (3^2) × (3^x)^3
Since log15 243 = x, we can rewrite the expression as:
243 = (3^2) × (3^x)^3
Taking the logarithm of both sides, we get:
log243 = log[(3^2) × (3^x)^3]
Using the properties of logarithms, we can simplify the expression:
log243 = log(3^2) + log[(3^x)^3]
Applying the power rule of logarithms, we have:
log243 = 2log3 + 3log(3^x)
Since log155 = x, we can substitute the value of x:
log243 = 2log3 + 3log15
Therefore, the value of log15 243 in terms of x is 3log15, which is option D.
Let's start by expressing 243 as a product of powers of prime numbers:
243 = 3 × 3 × 3 × 3 × 3 = 3^5
Now, let's express 15 as a power of a prime number:
15 = 3 × 5
So, we can write 243 as a power of 15:
243 = (3^5) = (3 × 3 × 3 × 3 × 3) = (3^2) × (3^3) = (3^2) × (3 × 3 × 3) = (3^2) × (3^1 × 3^1 × 3^1) = (3^2) × (3^1)^3 = (3^2) × (3^x)^3
Since log15 243 = x, we can rewrite the expression as:
243 = (3^2) × (3^x)^3
Taking the logarithm of both sides, we get:
log243 = log[(3^2) × (3^x)^3]
Using the properties of logarithms, we can simplify the expression:
log243 = log(3^2) + log[(3^x)^3]
Applying the power rule of logarithms, we have:
log243 = 2log3 + 3log(3^x)
Since log155 = x, we can substitute the value of x:
log243 = 2log3 + 3log15
Therefore, the value of log15 243 in terms of x is 3log15, which is option D.
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If log155 = x, what is the value of log15 243 in terms of x?a)3xb)3 - ...
Answer is D
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If log155 = x, what is the value of log15 243 in terms of x?a)3xb)3 - 3xc)3x - 5d)5 - 5 xCorrect answer is option 'D'. Can you explain this answer?
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