Question

find the base 10 logarithms of a) square root 1000 b) 10/ cube root of 10 c) 10^a/10^-b

Answer 1

\[a) \lg(\sqrt(10)^{3} )= \lg((10)^{3})^{1/2} =\lg(10\sqrt{10})\]

Answer 2

Express \[\sqrt{1000}\] as an power with rational exponent: note that 1000=\[10^{3}\]. \[\sqrt{10^{3}}=10^{3/2}\].
A logarithm is an exponent! So log \[\sqrt{1000}=\log 10^{3/2}=3/2\]..
b) 10/\[10/\sqrt[3]{10}=10^{1}/10^{1/3}.\]
Using quotient rule, this =\[10^{3/3-1/3}=10^{2/3}.\].
Therefore, \[\log10^{2/3}=2/3.\].
Hope that helped for the first two. The third one is like b), but the answer will have a variable answer.

Answer 3

ah thank you so much! and do you think c may be a+b ??
but thanx for the help!

Answer 4

yes you think right