A line with a slope of -7 passes through the points (u,0) and (8,-7) what is the value of u?
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I assume there are some plus signs that aren't rendering for some reason, so that the plane should be 
.
You're minimizing
subject to the constraint 
. Note that 
and 
attain their extrema at the same values of 
, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is
Take your partial derivatives and set them equal to 0:
Adding the first three equations together yields
and plugging this into the first three equations, you find a critical point at
.
The squared distance is then
, which means the shortest distance must be 
.
You're minimizing
The Lagrangian is
Take your partial derivatives and set them equal to 0:
Adding the first three equations together yields
and plugging this into the first three equations, you find a critical point at
The squared distance is then
The equation which shows the true solution to the given logarithmic equation is,
The power of the log rule says that the number written in the front of the logarithmic function can be raised to the power of the logarithmic function.
For example,
Given information-
The logarithmic equation given in the problem is,
Using the power rule of the logarithmic function,
Using the exponent rule of the logarithmic function the above equation can be written as,
Solve it further,
Hence, the equation which shows the true solution to the given logarithmic equation is,
Learn more about the rules of logarithmic function here;