Very simple symbol question regarding a logarithmic function (I can't find it)

In summary, the solution to finding log(3)9 is to substitute x = 2 into the equation 3^x = 9, which can be represented as log(3)9 = 2. The leftwards arrow next to the x is most likely indicating that x = 2 is the solution or that it follows from the equation. The notation used may not be standard, but it is the author's way of representing the solution.
  • #1
singleton
121
0
Well I have this leftwards arrow in my book describing the solution to a logarithmic function and I've not seen it thus far and (if I was ever introduced to it) have since forgot what it means!

When asked to find log(3)9
3^x = 9
3^x = 3^2
<--x = 2
log(3)9 = 2

I'm not sure what the leftwards arrow beside the x is for :(

Please forgive my logarithmic notation, I'm aweful with latex(?) so please note that 3 is the base (so I separated it in brackets).
 
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  • #2
I don't think there is anything "standard" there. It's just the author's way of telling you to substitute the value x = 2 into the equation or that x = 2 is the solution.
 
  • #3
I'll take a guess: "it follows from".
 

1. What is a logarithmic function?

A logarithmic function is a mathematical function that represents the inverse of an exponential function. It is commonly written as y = logb(x), where b is the base of the logarithm.

2. How do you graph a logarithmic function?

To graph a logarithmic function, you can plot several points on a coordinate plane and then connect them with a smooth curve. The vertical asymptote of the graph will be the y-axis, and the x-intercept will be the x-value of the base.

3. What is the domain and range of a logarithmic function?

The domain of a logarithmic function is all positive real numbers, and the range is all real numbers.

4. How do you solve equations involving logarithmic functions?

To solve equations involving logarithmic functions, you can use inverse operations to isolate the variable. Remember to check for extraneous solutions, as logarithmic functions have restrictions on their domain.

5. What is the relationship between logarithmic and exponential functions?

Logarithmic and exponential functions are inverse functions of each other. This means that if we have an equation y = logb(x), we can rewrite it as x = by, where b is the base of the logarithm. This relationship is also reflected in their respective graphs, where they are mirror images of each other across the line y = x.

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