Solve the equation
3^5sqrt(x+2)^3+3=27
My answer is 30
3 ^5√(x+2)^3 +3=27
isolate the radical
3 ^5√(x+2)^3 =24
divide by 3
^5√(x+2)^3 =8
set the radical to the power of 5 to cancel out the sqrt and also set 8 to the power of 5
(x+2)^3 = 32768
cube root to cancel out the exponent of three
x+2=32
-2
x=30
i hope that made sense, idk if it’s right
Well, that's quite ambitious! But I'm afraid your answer missed the mark. Let's break it down:
First, we need to get rid of the square root. To do that, we can raise both sides of the equation to the power of 2/3.
(3^5(sqrt(x+2))^3 + 3)^2/3 = 27^(2/3)
Now, simplify!
3^5(sqrt(x+2))^2 + 3 = 9
Next, let's isolate (sqrt(x+2))^2.
3^5(sqrt(x+2))^2 = 9 - 3
We end up with:
243(x+2) = 6
To find x, divide both sides by 243:
(x+2) = 6/243
Simplify:
(x+2) = 1/41
Subtract 2 from both sides:
x = -79/41
So, the solution is actually -79/41, not 30! Keep practicing, mathematician in the making!
To solve the equation 3^(5√(x+2))^3 + 3 = 27, we need to follow a series of steps. Let's break it down:
Step 1: Subtract 3 from both sides of the equation to isolate the term with the exponent:
3^(5√(x+2))^3 = 27 - 3
3^(5√(x+2))^3 = 24
Step 2: Take the cube root of both sides to remove the exponent:
cuberoot(3^(5√(x+2))^3) = cuberoot(24)
3^(5√(x+2)) = cuberoot(24)
Step 3: Simplify the right side of the equation:
3^(5√(x+2)) = cuberoot(24)
Step 4: Take the natural logarithm (ln) of both sides of the equation:
ln(3^(5√(x+2))) = ln(cuberoot(24))
Step 5: Use the property of logarithms to bring down the exponent:
(5√(x+2))*ln(3) = ln(cuberoot(24))
Step 6: Divide ln(3) from both sides to solve for (x+2):
5√(x+2) = ln(cuberoot(24))/ln(3)
Step 7: Square both sides of the equation to eliminate the square root:
(5√(x+2))^2 = (ln(cuberoot(24))/ln(3))^2
Step 8: Simplify both sides of the equation:
25(x+2) = ((ln(cuberoot(24))/ln(3))^2
Step 9: Divide both sides by 25 to solve for (x+2):
x+2 = ((ln(cuberoot(24))/ln(3))^2)/25
Step 10: Subtract 2 from both sides to find the value of x:
x = ((ln(cuberoot(24))/ln(3))^2)/25 - 2
Now, by substituting the value of (ln(cuberoot(24))/ln(3)) into the equation, we can find the value of x.
I got 36.9, don't quote me but I'll post a brainly and ask a tutor
thank you
Did you sub in the value of 30 to see if you are correct?
Following the order of operations, I get:
left side = 243(√32)^3 + 3
= appr 43990.7 , certainly ≠ 27
3^5sqrt(x+2)^3+3=27
3^5sqrt(x+2)^3 = 24
243√(x+2)^3 = 24
√(x+2)^3 = 8/81
(x+2)^(3/2) = 8/81
x+2 = (8/81)^(2/3) = appr .2137
x = appr -1.7863