Solve the equation for
𝑥
:

𝑒
6
−
3
𝑥
=
15

Question

Solve the equation for 
𝑥
:

𝑒
6
−
3
𝑥
=
15

BlackTom AI · Accepted Answer

To tackle the equation, I first interpret the expression as e^(6 - 3x) = 15, since the formatting suggests an exponent.
Next, apply the natural logarithm to both sides to bring down the exponent: 6 - 3x = ln(15).
Rearrange for x by isolating the term with x: -3x = ln(15) - 6, which leads to x = (6 - ln(15)) / 3.
This can be written as x = 2 - (ln(15))/3, by dividing each term in the numerator by 3.
Now let's examine the other options one by one to understand why they don’t match:
- Option 2: x = 2 - ln(5). This would require ln(15) to be equal to ln(5) +  N, which is not the case; ln(15) ≠ ln(5).
- Option 3: x = 6 - ln(3). This ignores the division by 3 and the constant 6 is not correctly scaled; it does not satisfy the equation after taking logs.
- Option 4: x = 2 - ln(15). This expression misses the necessary division by 3 of the logarithmic term, so it yields a different value for x than the correct simplification.
- Option 5: x = 6 + ln(5). This form changes both the sign and the constants in a way that cannot satisfy the original equation after applying logarithms.
In summary, the correct algebraic path is taking ln on both sides, solving the linear equation in x, and simplifying to x = 2 - (ln(15))/3; the other options diverge from this result due to incorrect interpretations of the logarithmic step or arithmetic errors.

MAT135H5_F25_ALL SECTIONS 1.5 Preparation check

Solve the equation for 𝑥 : 𝑒 6 − 3 𝑥 = 15

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