In Exercises 9–20, write each equation in its equivalent logarith...

Question

In Exercises 9–20, write each equation in its equivalent logarithmic form. ∛8 = 2

Accepted Answer

Hey everyone welcome back in this problem we are asked which of the following is a logarithmic form of the fourth root of 1296 equals six. Okay so we have the fourth root 1296 equals six. Okay now we were looking for the log rhythmic form so let's recall one of our log rules. We have a log rule that says if we have something B to the exponent A. Equals some quantity X. This is equivalent to writing log base B. Of X is equal to A. Okay so that's our longer than role. Now when we're looking at this quantity or this expression, this equation on the left here. Well it looks similar to the expression we've been given or the equation we've been given. Okay but in the one here in red we have B to an exponent A. In ours we have a root. So let's try to get our expression our equation to look like the one in red. So that we can use the log rhythm rule. Alright now let's recall if we have the end through of some quantity. M. We can write this as M. to the exponent one over N. Okay well look what we have here. Now we can apply this to the left hand side of our expression. So the fourth root of 1296 is the same as writing 1296 all to the exponent 1/4. Okay that's equal to six. Alright so now our equation looks just like this red one and we can apply the rule. So be in our case is the base of the exponent. That's gonna be 1296 A. Is gonna be what's in the exponents? So that's gonna be 1/4 and X. Is gonna be the value by itself on the right hand side. Well that's six. Okay so rewriting that gives us log B. 1296 Of X six is equal to a. Which again was the exponent 1/4. So now we've rewritten our equation and long rhythm performed. We have log base 1296 oh six is equal to 1/4. That's gonna give us answer. A. Alright thanks everyone for watching.

In Exercises 9–20, write each equation in its equivalent logarithmic form. ∛8 = 2

Key Concepts

Exponential and Logarithmic Relationships

Understanding Roots and Exponents

Logarithmic Notation

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