How do you solve 3log5 125 - log2 8 equals x?

Answer 1

To solve the equation 3log5 125 - log2 8 = x, you can use the properties of logarithms. First, simplify the logarithmic expressions: 3log5 125 simplifies to log5 (125^3), and log2 8 simplifies to log2 (2^3). This gives you log5 15625 - log2 8 = x. Then, you can combine the logarithms using the quotient rule to get log5 (15625/8) = x. Finally, simplify the expression inside the logarithm to get x = log5 1953.125.

Answer 2

Well, darling, first you simplify that mess by using the power rule of logarithms. So, 3log5 125 becomes log5 125^3, and log2 8 is just log2 2^3. Then, you simplify further to get log5 625 - log2 8 = x. Finally, you calculate the logs to get x = 4 - 3, which equals 1. Voilà!

Answer 3

Your calculator won't usually have a function to calculate logs in base 5 or base 8 directly, but this can easily be solved. For example:

log5125 = log 125 / log 5 (taking both logs in base 10, or both logs in base e)

In this particular case, you can also solve the equation mentally - you don't even need a calculator! Just use the definition of a log: "To what power must I raise 5 to get 125?" The answer to this is, by definition, log5125. Similarly with log28.