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please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(2a+b) reduces to?
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please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(...
There is no single solution.Taking logs: alog3=blog5 and blog5=clog75 If alog3=blog5=t then a=t/log3, b=t/log5 leading to c=t/log75. Then ab-c(2a+b) =t^2/(log3log5) - (t/log75)(2t/log3+t/log5) =t^2[ 1/(log3log5) - (1/log75)[2log5+log3]/(lo3log5) =t^2[1/(log3log5) - (1/log75)[log75]/(log3log5) =t^2[ 1/(log3log5) - 1/(log3log5)] =0
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please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(...
Problem Statement:
If 3^a = 5^b = 75^c, then what is the value of ab - c(2a + b)?
Solution:
Given: 3^a = 5^b = 75^c
We can rewrite 75 as 3^1 * 5^2, so the equation becomes:
3^a = 5^b = (3^1 * 5^2)^c
Now, we can rewrite this equation as:
3^a = 3^c * 5^2c (using the property of exponents)
Since the bases are the same, the exponents must be equal:
a = c + 2c
Simplifying the above equation, we get:
a = 3c
Similarly, we can rewrite the equation as:
5^b = 3c * 5^2c
Again, equating the exponents:
b = 2c
Calculating the value of ab - c(2a + b):
ab - c(2a + b) = (3c)(2c) - c(2(3c) + 2c)
= 6c^2 - c(6c + 2c)
= 6c^2 - c(8c)
= 6c^2 - 8c^2
= -2c^2
Hence, the value of ab - c(2a + b) is -2c^2.
Summary:
The value of ab - c(2a + b) reduces to -2c^2.
If 3^a = 5^b = 75^c, then what is the value of ab - c(2a + b)?
Solution:
Given: 3^a = 5^b = 75^c
We can rewrite 75 as 3^1 * 5^2, so the equation becomes:
3^a = 5^b = (3^1 * 5^2)^c
Now, we can rewrite this equation as:
3^a = 3^c * 5^2c (using the property of exponents)
Since the bases are the same, the exponents must be equal:
a = c + 2c
Simplifying the above equation, we get:
a = 3c
Similarly, we can rewrite the equation as:
5^b = 3c * 5^2c
Again, equating the exponents:
b = 2c
Calculating the value of ab - c(2a + b):
ab - c(2a + b) = (3c)(2c) - c(2(3c) + 2c)
= 6c^2 - c(6c + 2c)
= 6c^2 - c(8c)
= 6c^2 - 8c^2
= -2c^2
Hence, the value of ab - c(2a + b) is -2c^2.
Summary:
The value of ab - c(2a + b) reduces to -2c^2.
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please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(2a+b) reduces to?
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please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(2a+b) reduces to? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(2a+b) reduces to? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(2a+b) reduces to?.
please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(2a+b) reduces to? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(2a+b) reduces to? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for please Help me in this questionIf 3^a=5^b=75^c then the value of ab-c(2a+b) reduces to?.
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