Joanne C. answered • 04/11/24
Enthusiastic Math and Science Tutor with over 20+ years of experience
Hi Latasha,
Use the Laws of logarithms to rewrite the expression
log3(x17⋅3√y14)
in a form with no logarithm of a product, quotient or power.
To solve this you will need the following rules of Logarithms
The power Rule logamn = n loga m // The exponent becomes a coefficient of the log
The product Rule loga mn = logam + logan
Log of same number as base logaa = 1
log3(x17⋅3√y14) // start with the product rule
log3 x17 + log3 3 + log3 √y14 // Now use the power rule
17 log3 x + log33 + 14/2 log3y // Note that √y14 = y(14/2)
17 log3 x + log33 + 7 log3y // Now use log of same number as base
17 log3 x + 1 + 7 log3y
