Write the expression as a single logarithm

Mathematics

1 answer:

viva [34]3 years ago

5 0

We have to use the following log rules here

$a log (b) = log b^a , log(a) + log(b) = log(ab), log (a)-log(b) = log(a/b)$

So for the given question , that is

$18log \sqrt x +9 log \sqrt [3]{x}-log 10 = log(x^{18/2}) + log(x^{9/3})-log 10$

$log(x^9)+log(x^3)-log 10= log(x^9*x^3)-log 10$

$=log(x^{12}) - log 10 = log(\frac{x^{12}}{10})$

You might be interested in

The path from the whales to the sharks is parallel to the path from the penguins to the stingrays. What is the distance between

gulaghasi [49]

The distance between the penguins and the stingrays which is parallel to the path from the whales to the sharks is 28 ft.

<h3>What is proportional segment between parallel lines?</h3>

In two triangle in which the one side of the first triangle is parallel to the one side of the other triangle, two similar triangle formed.

Due to this similar triangle the segment formed by the parallel line are proportional segment.

The path from the whales to the sharks is parallel to the path from the penguins to the stingrays.

The map of the zoo is attached below.

The distance from whale to shark is 18 ft, and this side is parallel to the path from the penguins to the stingrays. Suppose the distance between the penguins and the stingrays is x meters.

Thus, in the given triangle, the ratio of these two sides will be equal to the ratio of their corresponding sides. Hence,

$\dfrac{x}{18}=\dfrac{42}{27}\\x=\dfrac{42}{27}\times18\\x=28\rm\; ft$

Thus, the distance between the penguins and the stingrays which is parallel to the path from the whales to the sharks is 28 ft.

Learn more about the similar triangle here;

brainly.com/question/14285697