Number 2 says Write the given equation in exponential form. Log8 1/512=-3
1 answer:
In exponential form it is given as, 8⁻³ =
<u>Step-by-step explanation:</u>
We have to write the given equation in the exponential form, that is in the form of base to the power value.
Given:
log₈ ( ) = -3
Here the base is 8.
In the exponential form, it is written as,
base to the power 3 = 512
Here the reciprocal of 512 is given, so,
base to the power -3 =
So the exponential form is given as, 8⁻³ =
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Please find the attached diagram for a better understanding of the question.
As we can see from the diagram,
RQ = 21 feet = height of the hill
PQ = 57 feet = Distance between you and the base of the hill
SR= h=height of the statue
=Angle subtended by the statue to where you are standing.
= which is unknown.
Let us begin solving now. The first step is to find the angle which can be found by using the following trigonometric ratio in
:
Which gives to be:
Now, we know that and
can be added to give us the complete angle
in the right triangle
.
We can again use the tan trigonometric ratio in to solve for the height of the statue, h.
This can be done as:
Thus, the height of the statue is approximately, 8.45 feet.
