1/2log25 + 2/3log8 - 1/4log16 all to base 10. How do we work this out? Answer is 3/2, but I keeo getting 10

Question

1/2log25 + 2/3log8 - 1/4log16 all to base 10. How do we work this out? Answer is 3/2, but I keeo getting 10

Answer 1

Let's try this Raj ... Note all of the arguments (25, 8, 16) are powers of some simple integers,

so let's put that to work for us.

 

1/2log25 + 2/3log8 - 1/4log16 =

 

1/2 log 5^2 + 2/3 log 2^3 - 1/4 log 2^4 =  Now let's use the power rule: log_bx^e = elog_bx.

 

2(1/2) log 5 + 3(2/3) log 2 - 4(1/4) log 2 =

 

log 5 + 2log2 - log2 = 

 

log 5 + log 2 =                                           Now use the sum rule: log_bx + log_by= log_bxy

 

log (5x2) = log 10                                      Since the base is also ten, then

 

log 10 = 1                                                 You can check this out with a calculator. Looks like the

                                                                key was wrong. This time its not you, its THEM! you just

                                                                made a careless mistake.

 

Keep up the good work! Don't let algebra get you down' keep facing up to it!

 

 

 

 

Answer 2

(1/2 log₁₀ 25) + (2/3 log₁₀ 8) -(1/4 log₁₀ 16)

 

log ₁₀ 25^1/2 + log ₁₀ 8^2/3 - log ₁₀ 16^1/4

 

log ₁₀5 + log ₁₀ 4 - log ₁₀ 2 -----> log ₁₀ (4*5)/2 = log ₁₀ 20/2 -----> log ₁₀ 10 = 1