help express as a logarithm of a single value

Question

how do I express as a logarithm of a single value:

 

 

1.  log₂5 + log₂8

 

 

2.  3log₁₀6

 

 

give the logarithms for log 1000

 

 

thanks

Answer 1

1)  The identity you need is log(ab) = log(a) + log(b)

 

log₂5+log₂8 = log₂(8*5) = log₂40

 

2)  The identity you need for this one is: log(a^b) = b*log(a)

 

3log₁₀6 = log₁₀(6³) = log₁₀(216)

 

3) You need to know 2 things: 1000 = 10³ and log₁₀(10) = 1

 

log₁₀(1000) = log₁₀(10³) = 3log₁₀(10) = 3