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AP Precalculus Full Practice Exam 3 Section II Part B

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The functions $$g$$ and $$h$$ are given by

$$g(x)=3\\log a-2\\log b+\\frac{1}{2}\\log a+\\log_{10}c$$

$$h(x)=\\sec^2 x\\tan x-\\tan x$$

(A) i. Rewrite $$g(x)$$ as a single logarithm with base $$10$$ without negative exponents. Your answer should be in the form $$\\log(\\text{expression})$$

ii. Rewrite $$h(x)$$ as an expression in which $$\\tan x$$ appears once and no other trigonometric functions are involved.

(B) The functions $$j$$ and $$k$$ are given by

$$j(x)=2\\csc^2 x-3$$

$$k(x)=5e^{4-2x}+1$$

i. Solve $$j(x)=1$$ for all values of $$x$$ in the interval $$[0,2\\pi)$$.

ii. Solve $$k(x)=6$$ for all real values of $$x$$. Express your answer exactly.

$$a(x)=4-2\\sec(2x)$$ $$b(x)=1+\\sec(2x)$$

Find all values of $$x$$ in the interval $$[0,2\\pi)$$ for which $$a(x)=b(x)$$.

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Section II Part B

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