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

1. log

_{2}5 + log_{2}82. 3log

_{10}6give the logarithms for log 1000

thanks

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

1. log_{2}5 + log_{2}8

2. 3log_{10}6

give the logarithms for log 1000

thanks

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Olney, MD

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

log_{2}5+log_{2}8 = log_{2}(8*5) = log_{2}40

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

3log_{10}6 = log_{10}(6^{3}) = log_{10}(216)

3) You need to know 2 things: 1000 = 10^{3} and log_{10}(10) = 1

log_{10}(1000) = log_{10}(10^{3}) = 3log_{10}(10) = 3

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