Q. Find the numerical value of the log expression.loga=8logb=2logc=−4loga9b9c8Answer:
Apply Quotient Rule: We are given the values of loga, logb, and logc, and we need to find the value of log(a9b9c8). We can use the properties of logarithms to simplify the expression.First, let's apply the quotient rule of logarithms, which states that log(ba)=log(a)−log(b).log(a9b9c8)=log(c8)−log(a9b9)
Apply Product Rule: Now, let's apply the product rule of logarithms to the second term, which states that log(ab)=log(a)+log(b). log(a9b9)=log(a9)+log(b9)
Apply Power Rule: Next, we apply the power rule of logarithms, which states that log(an)=nlog(a), to each term.log(c8)=8log(c)log(a9)=9log(a)log(b9)=9log(b)
Substitute Given Values: Now we substitute the given values of loga, logb, and logc into the expression.log(c8)−(log(a9)+log(b9))=8⋅log(c)−(9⋅log(a)+9⋅log(b))=8⋅(−4)−(9⋅8+9⋅2)
Perform Arithmetic Operations: We perform the arithmetic operations.=−32−(72+18)=−32−90=−122
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