Question

Select true or false for each statement.

Statement 1: log3(vwx) = log3v + log3w - log3x

True or False?

Statement 2: log4n + 3log4m = log4(nm³)

True or False?

Statement 3: 13(log2c log2d) - 4log2e = log2(cd3e4)

True or False?

Answer 1

Statement 1 is true, Statement 2 is true, Statement 3 is true.

Step-by-step explanation:

Statement 1: True. The given equation follows the property of logarithms that states log(ab) = log(a) + log(b). Therefore, log3(vwx) = log3(v) + log3(w) + log3(x)

Statement 2: True. Using the property log(ab) = log(a) + log(b), we can simplify log4(n) + 3log4(m) to log4(nm³).

Statement 3: True. By applying the property log(ab) = log(a) + log(b), we can simplify 13(log2(c)log2(d)) - 4log2(e) to log2((c^13)(d^13)/(e^4)).