Mark Shepherd

Mark Shepherd

Answered question

2022-06-14

Answer & Explanation

nick1337

nick1337

Expert2023-05-21Added 777 answers

To solve the equation 42.0541.5=(31x)1.08, we'll follow these steps:
Step 1: Simplify the left-hand side of the equation
We have 42.0541.5. To simplify this expression, we divide 42.05 by 41.5:
42.0541.51.0120481927710844.
So the left-hand side of the equation simplifies to approximately 1.0120481927710844.
Step 2: Simplify the right-hand side of the equation
We have (31x)1.08. To simplify this expression, we raise 31x to the power of 1.08:
(31x)1.08=1.08(31x)1.08.
Step 3: Equate the two sides of the equation
Now we equate the simplified left-hand side and right-hand side of the equation:
1.0120481927710844=1.08(31x)1.08.
Step 4: Solve for x
To solve for x, we'll isolate the variable by dividing both sides of the equation by 1.08:
1.01204819277108441.08=(31x)1.08.
Simplifying the left-hand side:
1.01204819277108441.080.9387543252595155.
Step 5: Isolate x and solve
To isolate x, we'll take the 1.08th power of both sides:
(1.01204819277108441.08)1.08=((31x)1.08)1.08.
Simplifying the right-hand side:
((31x)1.08)1.08=31x.
Now, we'll solve for x by isolating it. Multiply both sides of the equation by x:
x×(1.01204819277108441.08)1.08=31.
Finally, divide both sides by (1.01204819277108441.08)1.08 to solve for x:
x=31(1.01204819277108441.08)1.0833.03244435832572.
Therefore, the approximate value of x that satisfies the equation is x33.03244435832572.

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