Question

Which properties are present in a table that represents a logarithmic function in the form y=logb^x when b>1

Answer 1

See in the explanation

Explanation:

In this case we have the following equation:

$y=logb^x \ when \ b>1$

By Power Property, we know that:

$log_{a}u^n=nlog_{a}u$

So applying this property to our equation:

$y=xlogb \\ \\ or \\ \\ \boxed{y=(logb)x}$

So this is the equation of a line that passes through the origin and whose slope is logb.

For example, suppose $b=10$, therefore:

$logb=log10=1$

Therefore, we can write the equation of a line whose slope is $m=1$. Then, a table would look like:

$\begin{array}{cc}x & y=(log10)x\\0 & 0\\1 & 1\\2 & 2\\3 & 3\end{array}$

Learn more:

x and y intercepts of a line: https://brainly.com/question/13770925#

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Answer 2

Answer:

The table is missing, however this can be solved by exploring all properties of a logarithmic function. First of all, we have to consider that properties for logarithmic functions are the same as actual logarithms.

A logarithmic function is the inverse of a exponential function, this means that it's closely related to exponent properties, which are:

$x^{m} x^{n}=x^{m+n} \\\frac{x^{m} }{x^{n} }=x^{m-n} \\(x^{m})^{n}$

Another important properties are directly related with logarithms:

• Logarithm of a product: $log_{a}(MN)=log_{a}M+  log_{a}N$
• Logarithm of a quotient: $log_{a}\frac{M}{N}=log_{a}M-log_{a}N$
• Logarithm of a power: $log_{a}M^{n}=n.log_{a}M$

If you compare these 6 properties you will find similarities that help students to memorize them easily. For example, you can say that product related to adding, division relates to subtracting and power relates to multiplying.

Lastly, another important property is actually the relation between logarithmic and exponential functions:

$y=a^{x} \equiv log_{a}y=x$

So, there you have all needed properties to analyse, operate and transform logarithmic functions.