lg10^3=3 true or false?

log(base 2)16=8 true or false?

log(base 4)2=1/2 true or false?

2log(base 2)^47=47 true or false?

log(base 3)9 + log(base3)1/27=1/2 true or false?  

help

Write these into exponential notation and check ...

    log_bN = x     in exponential notation is    b^x = N

In common logs, the base is 10 but it usually isn't written. I am going to write it so it is clear.

log₁₀(10³) = 3         written in exponential notation is  10³ = 10³               Is this true?

log₁₀(1/10) = 0,1    written in exponential notation is  10^0,1  =  1/10          Is this true?

10^log₁₀7 = log₁₀7     written in exponential notation is  10^log₁₀7 = log₁₀7     Is this true?

log₁₀(1/10)³ = -1/3  written in exponential notation is  10^-1/3 = (1/10)³       Is this true?