SOLUTION: Log (base of square root 3) (square root of 9 with a 3 on the root in front) ^5x

Question 238433: Log (base of square root 3) (square root of 9 with a 3 on the root in front) ^5x
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

If this is incorrect, please repost using parentheses to make things clearer. (BTW, is called "the cube root of 9")

There is no equals sign. Is there supposed to be one? If yes, please repost with the entire equation. Without an equals sign this is just an expression and all you can do with an expression is simplify it.

All roots can be written as fractional exponents and rewriting the cube root of 9 as a fractional power of 9 will help us simplify:

Using the property of exponents, , on this we get:

Now we can use the property of logarithms, , to move the exponent in the argument out in front:

And finally we need to figure out the logarithm: . We could use changing the bases and then using calculators. Or we could just be clever. If you understand what logarithms represent, you know that represents the exponent for that results in 9. So what is "the exponent for that results in 9"? Well and So . So "the exponent for that results in 9" is 4. Substituting this in for we get:

which simplifies to

RELATED QUESTIONS
square root over -8 over 27 there is a small 3 in front of the square root sign too. (answered by praseenakos@yahoo.com)

Hello. May I get your help on solving this logarithm question? I got stuck while doing it (answered by MathTherapy)

what is log base 9 of the square root... (answered by lwsshak3)

1)Solve for X log(Square root of 5)(x) =6 -I am not sure how to put in a square root... (answered by josgarithmetic)

log of 9 to the base square root of x - log of 3 to the base x = 9 + 6 log of x to the... (answered by kiru_khandelwal)

log base 9 cubed root of... (answered by jsmallt9,MathTherapy)

Square root of 7x-1 = square root of 5x +... (answered by Alan3354)

Log( base 3) square root... (answered by ewatrrr)

3 square root of 5 + 9 square root of... (answered by longjonsilver)