Question

Given log2=0.3010, log3=0.4771, log5=0.6690, and log7=0.8451...
Find a.) log8 b) log5/7 c.) log1.5 d.) log3/14 e) log12

I didn't know how to do b, c, and d. I also don't know if log 12 is right.

Answer:
a.) 0.903
b.)?
c.)?
d.)?
e.) 1.0791

Answer 1

i figured C. I'm really stuck on b &d. btw. I can't use a calculator to figure these because we aren't supposed to. How do you find it out w/o using calc.

Answer 2

a) correct
b) log(5/7)
= log 5 - log 7
you have both of these, just do the subtraction

c) log 1.5
= log (3/2)
= log3 - log 2
you have both of these

d) log (3/14)
= log(3/( (2)(7) )
= log 3 - log2 - log 7
again, you have those 3 values

log 12
= log(4 x 3)
= log 4 + log3
= log 2^2 + log3
= 2log2 + log3
= 2(.3010) + .4771
= .6020 + .4771
= 1.0791

so far I have not used my calculator
check: by calculator, log 12 = 1.0792