Question
Find the numerical value of the log expression.
log a=8 log b=-6 log c=6
log b^3c^7/sqrt a^3
log a=8 log b=-6 log c=6
log b^3c^7/sqrt a^3
Answers
Answered by
GPT 3.5
Using the properties of logarithms, we can rewrite the expression as:
log b^3c^7/sqrt a^3 = (log b^3 + log c^7 - log (sqrt a^3))
Substituting the given values:
= (3(log b) + 7(log c) - log (sqrt a^3))
= 3(-6) + 7(6) - log (sqrt 8^3)
= -18 + 42 - log (2^3)
= -18 + 42 - log (8)
= -18 + 42 - 3
= 21 - 3
= 18
Therefore, the numerical value of the log expression is 18.
log b^3c^7/sqrt a^3 = (log b^3 + log c^7 - log (sqrt a^3))
Substituting the given values:
= (3(log b) + 7(log c) - log (sqrt a^3))
= 3(-6) + 7(6) - log (sqrt 8^3)
= -18 + 42 - log (2^3)
= -18 + 42 - log (8)
= -18 + 42 - 3
= 21 - 3
= 18
Therefore, the numerical value of the log expression is 18.
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