In exercise use properties of logarithms to expand each loga

In exercise, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. Log_5(7 middot 3) log_g(13 middot 7) log_7 (7x) log_9 (9x) log(1000 x) log(10,000 x) log_7 (7/x) log_9 (9/x) log(x/100) log(x/1000) log_4(64/y) log_5(125/y) ln(e^2/5) ln(e^4/8) log_6 x^3 log_b x^7 log N^-6 log M^-8 ln 5 squareroot x ln 7 squareroot x log_5 (squareroot x/25) log_6(36/squareroot x + 1) log_8(64/squareroot x + 1) log_b(x^2 y/z^2) log_b(x^3 y/z^2) log squareroot 100 x ln squareroot ex log 3 squareroot 3 x/y log 5 squareroot x/y log_b(squareroot xy^3/z^3 log_b(3 squareroot xy^4/z^5) log_5 3 squareroot x^2 y/25) log_2 5 squareroot xy^4/16 ln[10 x^2 3 squareroot 1 - x/7 (x + 1)^2] log [100 x^3 3 squareroot 5 - x/ 3(x + 7)^2] In Exercise 41-70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate as a single logarithmic expressions without using a calculator.

Solution

log₅(7*3)

Log_x(a*b)=log_xa+log_xb

So we get

Log₅(7*3)= log₅7 + log₅3

That\'s the required expansion