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