(0.005*i)+(0.01+0.03log(i))+(0.64+0.07*log(i))=1.298

Let's solve the given equation step by step:

The equation is:

\[
0.005i + (0.01 + 0.03\log(i)) + (0.64 + 0.07\log(i)) = 1.298
\]

### Step 1: Simplify the logarithmic terms
Combine the constants and the logarithmic terms:

\[
0.005i + 0.01 + 0.03\log(i) + 0.64 + 0.07\log(i) = 1.298
\]

Now, simplify further by combining like terms:

\[
0.005i + 0.65 + (0.03 + 0.07)\log(i) = 1.298
\]

\[
0.005i + 0.65 + 0.1\log(i) = 1.298
\]

### Step 2: Isolate the terms with the variable \( i \)
Subtract 0.65 from both sides:

\[
0.005i + 0.1\log(i) = 1.298 - 0.65
\]

\[
0.005i + 0.1\log(i) = 0.648
\]

### Step 3: Solve the equation numerically
This equation involves both linear and logarithmic terms, so solving it analytically is challenging. I'll solve this numerically to find the value of \( i \).

Let me calculate it.The solution to the equation is approximately \( i \approx 50.97 \).

Would you like more details about the steps, or do you have any specific questions?

Here are five related questions for deeper exploration:
1. How can logarithmic equations be solved graphically?
2. What are some applications of logarithmic equations in real-world scenarios?
3. How does the method of numerical approximation (like using `fsolve`) work?
4. What are the key differences between logarithmic and exponential functions?
5. Can this equation be simplified further using algebraic methods?

**Tip:** For equations involving both linear and logarithmic terms, numerical methods like Newton's method or tools like `fsolve` are often required to find approximate solutions.

The query submitted by the user:(0.005*i)+(0.01+0.03log(i))+(0.64+0.07*log(i))=1.298

Explore how to solve the equation 0.005i + (0.01 + 0.03log(i)) + (0.64 + 0.07log(i)) = 1.298 using a combination of logarithmic and linear methods. Learn about numerical approximation techniques for non-linear equations, suitable for Grades 11-12 and college-level students.

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