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Given that log_(b)(7)=1.946,log_(b)(9)=2.197, and log_(b)(16)=2.773, find the logarithm of log_(b)(1)/(63)

User NhatVM
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Final answer:

To compute the logarithm of a quotient, we use the properties of logarithms. Thus, log_(b)(1/63) becomes 0 - 2*log_(b)(7) - log_(b)(9). When we substitute the given values, we get log_(b)(1/63) equals -6.089.

Step-by-step explanation:

First, notice that 63 = 7^2 * 9. Using logarithm properties, log_(b)(1/63) = log_(b)(1) - log_(b)(63) = log_(b)(1) - log_(b)(7^2) - log_(b)(9). We know that log_(b)(1) = 0 (based on the property of logarithms), log_(b)(7^2) = 2*log_(b)(7), and log_(b)(9) = 2.197 based on the given values.

Next, let's substitute the numbers provided: log_(b)(1/63) = 0 - 2*1.946 - 2.197 = -6.089

So, the value of log_(b)(1/63) is -6.089.

Learn more about Logarithms properties

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