Algebra 2 Lesson #73 Solving Exponential and Logarithmic Equations

In this lesson, we will learn how to solve exponential and logarithmic equations using a variety of techniques. Solving an exponential equation generally requires taking the log of both sides and then isolating the variable. For the case of a logarithmic equation, where the two logarithms have the same base and are set equal, we can set the arguments equal to each other and solve.

[HastiinTliziYazhi]

At 11:58 is there any particular reason why you did not use the quotient property for logarithms to rewrite log(2)-log(5) as log(2/5)? For that matter, would it be permissible to rewrite the entire expression as -3log(2)-log(2)+log(5)? I wanted to double check whether fully simplifying mandates rewriting logarithmic expressions to be fully in terms of addition/subtraction or multiplication/division. Do we have to concern ourselves with that or is it more personal preference on the part of the instructor or test?