Question

Need some help with this things, i know basic stuff but I have to refresh my knowledge. So we have this equation: 3 * 10⁻2 x - 3.5 * 10²= 1.5 * 10² x + 100. It's a linear equation, right? I need a step-by-step guide on how to solve this. Then there is this equation: (20x⁰.25 - 4√(3))⁰.25 = 2 * √(3). Would love an in-depth explanation for both of them.

Answer 1

To solve linear equations or other equations involving exponents and roots, isolate variables, combine like terms, and apply the rules for exponents. Step-by-step, gradual simplification leads to the solution. For fractional or negative exponents, adjust the decimal point and apply arithmetic rules accordingly.

Step-by-step explanation:

The equation 3 * 10⁻² x - 3.5 * 10² = 1.5 * 10² x + 100 is indeed a linear equation. To solve it, follow these steps:

1. Start by adding '3.5 * 10²' to both sides of the equation to isolate the variable terms on one side and the constants on the other.
2. Then subtract '1.5 * 10² x' from both sides to get all x terms on one side.
3. Combine like terms and then divide by the coefficient of x to solve for the value of x.

For the equation (20x⁰.²⁵ - 4√(3))⁰.²⁵ = 2 * √(3), we follow a similar process:

1. Raise both sides of the equation to the power of 4 to get rid of the 0.25 exponent on the left side.
2. After simplifying, you will isolate x and solve for its value.

Remember, dealing with exponents involves application of the rules for multiplying, dividing, and raising powers to powers. If the exponents are negative, adjust the decimal point accordingly and treat the negative exponents as you would in regular arithmetic when adding or subtracting them.