Explain to Noah Clue why the following logarithmic properties are true. Be sure to demonstrate with examples and explain it well enough so that Noah could relay the information to Atta Loss with authority.

log (a*b) = log (a) + log (b)
log (a^b) = b * log (a) moi

Onnie is considering doing some long term investing with money that she inherited. she would like to have $50,000 at the end of 30 years. approximately how much money would lonnie need to put into an account earning 6% interest compounded annually in order to meet her goal?