Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

log (1000x)

Question

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

log (1000x)

anonymous · Answer

3+logx

anonymous · Answer

x = 1/1000

anonymous · Answer

log(1000x) <=> 1000x = e^0 <=> 1000x = 1, x = 1/1000

anonymous · Answer

the base is 10 not e,

anonymous · Answer

lnx is base e

anonymous · Answer

Then 1000x = 10^0 and continue from there to get x = 1/1000

Only in very remedial math does lnx mean to the base e, later on log means base e.

anonymous · Answer

but how can you prove it is base e or base 10, you have the question by your hand?

anonymous · Answer

It's not a question of proving anything, anything written as logx if it doesn't have a number for the base is assumed to be a natural log. The log to the base 10 is known as common log.