Answer:
To solve an exponential equation, take the log of both sides, and solve for the variable.
Step-by-step explanation:
Example 1: Solve for x in the equation tex2html_wrap_inline119 .
Solution:
Step 1: Take the natural log of both sides:
displaymath121
Step 2: Simplify the left side of the above equation using Logarithmic Rule 3:
displaymath123
Step 3: Simplify the left side of the above equation: Since Ln(e)=1, the equation reads
displaymath127
Ln(80) is the exact answer and x=4.38202663467 is an approximate answer because we have rounded the value of Ln(80)..
Check: Check your answer in the original equation.
displaymath131
3 blue birds
if he sees 5 more than blue 8 - 5 = 3
First, some housekeeping:
cos = 12/13 is incomplete; "cos" must have an argument (input).
cos x = 12/13 is fine; here "cos" has the argument (input) x.
Given that cos x = 12/13, find sin x. To do this, we'll need to find the length of the opposite side, given that the hypo length is 13 and the adj. side length is 12.
12^2 + opp^2 = 13^2, or opp^2 = 169-144 = 25.
Then the opp side could be either 5 or -5. Let's assume that it's +5, and that angle x is in the first quadrant.
Then sin x = opp / hyp = 5/13 (answer)
cos 2 is an entirely different kind of problem. Here you are told what the argument (input) to the cosine function is (it is 2, which here means 2 radians).
Using a calculator: cos 2 = -0.416. Note that the angle 2 rad is in QII, which is why the "adjacent side" is negative and also why the cos of 2 is negative.
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