Express 5^3 = x as a logarithmic equation.

Question

anonymous · Answer

5^3=x

mathmale · Answer

Here you have an expression in the form x= (base 5)^y.

In other words, 5 is the base of your exponential function here.

Take the log to the base 5 of both sides of the given expression to convert it into a logarithmic equation:$$\log_{5} (5^3)=\log_{5} x$$

mathmale · Answer

Note that the exponential and logarithmic functions are inverses of one another.  Use this fact to simplify the left side of the above equation.

Where have you seen expressions of the form$$\log_{a} a^n~before?$$

mathmale · Answer

How have you simplified them?

anonymous · Answer

log_5 125=x

anonymous · Answer

$$\log_{5} 125=x$$

mathmale · Answer

Actually, $$\log_{a} a^n=  n$$  In words, the log operator cancels out the work of the exponential function, leaving us with simply n (the exponent).

$$\log_{5} 5^4=?$$

anonymous · Answer

i'm confused

mathmale · Answer

What info do you need?  What would resolve your confusion?  
If you're working with exponential and logarithmic functions, then you have seen the topic "inverse functions" before.

anonymous · Answer

not really i'm trying to learn it now