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Given that logb(7)≈1.946, logb(9)≈2.197, and logb(16)≈2.773, find the logarithm of logb(1/63)

b is base b

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Final answer:

To find the logarithm of log(b)(1/63), we can apply the property of logarithms that states the logarithm of the quotient of two numbers is equal to the difference of their logarithms.

Step-by-step explanation:

To find the logarithm of logb(1/63), we can apply the property of logarithms that states the logarithm of the quotient of two numbers is equal to the difference of their logarithms. So, we have:

logb(1/63) = logb(1) - logb(63)

Since logb(1) = 0, we just need to find logb(63). Since 63 can be expressed as the product of 7 and 9, we can use the property of logarithms that states the logarithm of a product is equal to the sum of the logarithms of the factors:

logb(63) = logb(7) + logb(9)

Substituting the given values, we have:

logb(1/63) = 0 - (1.946 + 2.197) = -4.143

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