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)log3(12) − log3(28) + log3(63)(b)log4(40) − log4(32) − log4(20)
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.
Similar Questions
Find the exact value of each expression.(a)log5(25)(b)log218
Find the exact value of each expression(a) log2 64(b) log6136(c) log8 2(d) ln e√22. Find the exact value of each expression(a) log10 1.25 + log10 80(b) log5 10 + log5 20 − 3 log5 23. Find the exact value of each expression(a) 2(log2 3+log2 5)(b) e3 ln 2
Find the exact value of each expression.(a)ln1e (b)log17(17)
Apply the properties of logarithms to simplify the expressions: (Criteria A)a) log39+log327b) log28−log22c) 3log105−log1025d) lnx+lnye) logaan
Simplify the equation using laws of logarithms. log2(12)+log2(7)+log2(5)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.