Question

question 8.
if ( xy = 8 ), then to the nearest tenth, the value of ( 5log_{2}x + 5log_{2}y ) is ______.

Explanation:

Step1: Use logarithm property \( \log_a M + \log_a N = \log_a(MN) \)

First, factor out the common factor 5 from the expression \( 5\log_2 x + 5\log_2 y \). We get \( 5(\log_2 x + \log_2 y) \). Then, apply the logarithm product rule: \( \log_2 x + \log_2 y = \log_2(xy) \). So the expression becomes \( 5\log_2(xy) \).

Step2: Substitute \( xy = 8 \) into the expression

Now substitute \( xy = 8 \) into \( 5\log_2(xy) \), we have \( 5\log_2 8 \). Since \( 8 = 2^3 \), \( \log_2 8=\log_2 2^3 = 3 \) (because \( \log_a a^b = b \)). Then calculate \( 5\times3 = 15.0 \) (to the nearest tenth).

Answer:

15.0