The following function [math: f(x)] is logarithmic and has one [math: x] intercept.[math: f(x)=log] e[math: (10x+−7)+2] (10x+-7)+2 Calculate the value of [math: x] at the [math: x] intercept [math: (x,y)] (x, y) , correct to 3 decimal places.

Question

BlackTom AI · Accepted Answer

We’re asked to find the x-coordinate of the x-intercept for the function f(x) = ln(10x − 7) + 2, since the graph crosses the x-axis where f(x) = 0.

Option steps:
- Set f(x) to zero: 0 = ln(10x − 7) + 2.
- Isolate the natural log term: ln(10x − 7) = −2.
- Exponentiate both sides with base e to remove the ln: 10x − 7 = e^(−2).
- Solve for x: x = (7 + e^(−2)) / 10.

Now evaluate numerically: e^(−2) ≈ 0.135335283..., so 7 + e^(−2) ≈ 7.135335283, and dividing by 10 gives x ≈ 0.7135335283.

Rounding to 3 decimal places yields x ≈ 0.714.

Key checks:
- The argument of the logarithm, 10x − 7, must be positive; at x ≈ 0.7135, 10x − 7 ≈ 0.135, which is positive, so the solution is valid.
- The calculation uses natural logarithm (ln), as indicated by log_e, so the exponentiation step with e is appropriate.

The following function [math: f(x)] is logarithmic and has one [math: x] intercept.[math: f(x)=log] e[math: (10x+−7)+2] (10x+-7)+2 Calculate the value of [math: x] at the [math: x] intercept [math: (x,y)] (x, y) , correct to 3 decimal places.数值题

类似问题

A model that describes the association between the hours spent studying for an examand the mark achieved is: mark = 20 + 40 × log (hours) From this model, we would predict that a student who studies for 20 hours would scorea mark (to the nearest whole number) of:

The graph of the function [math: f(x)] is shown below.The rule for [math: f(x)] is most likely to be:

The x-intercept of the function is

The equation of the vertical asymptote for the function is

A model that describes the association between the hours spent studying for an examand the mark achieved is: mark = 20 + 40 × log (hours) From this model, we would predict that a student who studies for 20 hours would scorea mark (to the nearest whole number) of:

What is the equation of the graph shown?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单