Algebra Homework.?

Question

(1) Simplify into radical form:

(48x^3y^7)^1/2

(2) (9x^3)^1/2 / x^-2 . Simplify

(3) Solve exactly.

logx with base 3 + log5 base 3 = 2
(I hope i wrote that right or can it be written log base 3 (x) + log base 3 (5) =2.

Please help if you can. Thank you very much.

Answer 1

#1

sqrt ( 48 x^3 y ^7) = 4 x y^2 sqrt(3xy)

#2

x^2 sqrt(9 x^3) = 3 x^3 sqrt(x)

#3

Use the log rules: adding logs means you can multiply what's in the log function instead:
logbase3(5x) = 2

Raise both sides to the 3 power

3^logbase3(5x) = 9

Use the rule about how logs and exponents work to cancel:

5x = 9

x = 9/5

Answer 2

(48x^3y^7)^1/2

48 is 16*3 so this raised to the 1/2 power (or square root) is
4 (3^(1/2)) or 4 sqrt 3.

Square root of x^3 is x sqrt x [i.e. x (x^(1/2))]
Square root of y^7 is y^3 sqrt y.

So altogether,
(48x^3y^7)^1/2 = 4xy^3 sqrt 3xy OR 4xy^3 ((3xy)^1/2).

2. (9x^3)^1/2 / x^-2 . Simplify
(9x^3)^1/2 simplifies to 3x sqrt x
The denominator has a negative exponent which can be made positvie by bringing it to the numerator.
So the answer is,
3x^3 sqrt x

3. log base 3 (x) + log base 3 (5) =2.
log base 3 (x*5) = 2
log base 3 (5x) = 2
5x = 3^2
5x = 9
x = 9/5

Contact for more explanation.

Good luck :)

Answer 3

Question 1
48^(1/2).x^(3/2).y^(7/2)
= 4.√3.x^(3/2).y^(7/2)
= 4.√3.√(x³).√(y^7)
= 4√(3.x³.y^7)

Question 2
(9x³)^(1/2).x²
3x^(3/2).x²
3x^(5/2)
3.√(x^5)

Question 3
In the following , log means log to base 3:-
log x + log 5 = 2
log (5x) = 2
5x = 3²
5x = 9
x = 9 / 5

Answer 4

log(base 3) 5x=2

3^2=5x
9=5x
9/5=x

Let me know if u need explanation!

Whoops, forgot the first two
1.) (4xy^3)times square root of(3xy)

2.3x^3times square root of (x)