Find the exact value of each expression.(a)log3(12) − log3(28) + log3(63)(b)log4(40) − log4(32) − log4(20)

Question

Find the exact value of each expression.

(a) $\log_3(12) - \log_3(28) + \log_3(63)$

(b) $\log_4(40) - \log_4(32) - \log_4(20)$

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Solution

Sure, let's solve these logarithmic expressions step by step.

(a) log3(12) − log3(28) + log3(63)

According to the properties of logarithms, logb(m/n) = logb(m) - logb(n) and logb(m*n) = logb(m) + logb(n).

So, we can rewrite the expression as:

log3(12*63/28) = log3(27)

Since 3^3 = 27, the value of log3(27) is 3.

(b) log4(40) − log4(32) − log4(20)

We can rewrite this expression as:

log4(40/(32*20)) = log4(1/16)

Since 4^-2 = 1/16, the value of log4(1/16) is -2.

This problem has been solved

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