Find x
2x^(4/5) = 162
I don't understand this problem. Step by step would be great thank you :)
2x^(4/5) = 162
divide both sides by 2
x^(4/5) = 81
Raise both sides to the 5/4
(x^(4/5))^(5/4) = 81^(5/4) = (81^(1/4)^5
x = (the fourth root of 81)^5
= 3^5
= 243
To find x in the equation 2x^(4/5) = 162, we can start by isolating x.
Step 1: Divide both sides by 2 to get rid of the coefficient 2 on the left side of the equation:
(2x^(4/5)) / 2 = 162 / 2
Simplifying this equation gives:
x^(4/5) = 81
Step 2: To remove the exponent 4/5 on x, we can raise both sides to the reciprocal power, which in this case is 5/4. This will cancel out the exponent:
(x^(4/5))^(5/4) = 81^(5/4)
On the left-hand side, the exponents will multiply together:
x = 81^(5/4)
Step 3: Calculate 81^(5/4) using a calculator or by simplifying the expression. The exponent 5/4 means taking the fourth root of 81 and then raising it to the fifth power:
81^(5/4) = (81^(1/4))^5 = 3^5 = 243
Therefore, x = 243 is the solution to the equation 2x^(4/5) = 162.
To solve for x in the equation 2x^(4/5) = 162, we need to isolate x. Here's a step-by-step solution:
Step 1: Start by dividing both sides of the equation by 2 to eliminate the coefficient on the left side:
(2x^(4/5))/2 = 162/2
This simplifies to:
x^(4/5) = 81
Step 2: Now, we can remove the exponent by raising both sides of the equation to the reciprocal power of (4/5):
(x^(4/5))^(5/4) = 81^(5/4)
This simplifies to:
x = 81^(5/4)
Step 3: To evaluate 81^(5/4), we raise 81 to the power of 5/4:
x = (81)^(5/4)
Step 4: Simplify the right side of the equation by evaluating the exponent:
x = (3^4)^(5/4)
Since both the numerator and denominator of the exponent are divisible by 4, we can simplify further:
x = 3^(5)
Step 5: The final step is to evaluate 3^(5) by multiplying 3 by itself five times:
x = 3 * 3 * 3 * 3 * 3
Calculating this expression, we find that:
x = 243
Therefore, the solution to the equation 2x^(4/5) = 162 is x = 243.