50 =2×5×5
125=5×5×5
Hoghest common factor = 5×5
=25
The solution of the given exponential equation is 0.688.
Given that Mike is working on solving the exponential equation 37ˣ = 12.
An exponential equation is an exponential equation where the power (or) part of the exponent is a variable.
firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:
aˣ = y
logₐy = x
Now, we will apply this transformation to our equation and we get
log₃₇12=x
Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:
x=log12/log37
So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:
x≈1.079/1.568
x=0.688
Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.
Learn more about exponential equation from here brainly.com/question/24162621
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Answer:
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Step-by-step explanation:
For this case, we can model the problem as a rectangle triangle.
We know:
Height of the triangle.
Base of the triangle.
We want to know, angle between the hypotenuse and the base of the triangle.
For this, we use the following trigonometric relationship:

Clearing the angle we have:
Answer:
the angle of depression from the spotlight to the bottom of the door is:
A) 39 degrees