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Chapter 3.4 Pre Calculus Test DVC
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Exponential and Logarithmic Equations
Terms in this set (10)
Steps solving exponential equations
Step 1.) Determine the common base. Then reqrite both sides to have the same base.
Step 2.) Once the bases are the same, set the exponents equal to each other.
Step 3.) Solve the resulting equation
4^x=32
x=5/2
2^t=1/4
t=-2
e^3y+1= 3sqrt(e)
y=-2/9
Steps when we cannot rewrite the bases to be the same
Step. 1) Isolate the exponential function on one side of the equation
Step 2.)THINK LN, ln(e)^x=x or ln(M)^c=(C)ln(M)
Step 3.)Proceed to solve the varibale
Step 4.)Give an exact answer then round your answer with your calculator
3e^2x=5/3
x=0.26
5^(3x-1)=27
x=1.02
Solving the equation in the Form log(b) A= B
Step 1.) Make sure you one log on one side and a number on the other
Step 2.)Use definition of logarithm to rewrite the log y=log(b)^x ----> b^y=x
Step 4.) Check for extraneous solutions.
Solve for the equation using log(b) A=B log(2)x=7
2^7=x ,128=x ,log(base2)(128)= 7
solve for the equation using log(b) A=B log(6)(x+5)+log(6)x=2
x=4
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Verified questions
CALCULUS
Use Green’s first identity to prove Green’s second identity: ∫∫D (f∇^2g-g∇^2f)dA=∮C(f∇g - g∇f) · nds where D and C satisfy the hypotheses of Green’s Theorem and the appropriate partial derivatives of f and g exist and are continuous.
QUESTION
Find the differential of each function. $$ y=\ln (\sin \theta) $$
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Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3), i) using Definition 1, ii) using Equation 2
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An equation of motion of the form s = Ae^-ct cos(wt+δ) represents damped oscillation of an object. Find the velocity and acceleration of the object.
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