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UCLA MATH 3A - precalc3A

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Math 3A -- Prof. Wittman Pre-calc Review: Exponential & Logarithmic Functions Properties of Exponents zxzxbbb =+ xxbb1=− ()xzzxbb = The logarithm base b of a number x is the exponent we must raise b to get x. xbyxyb=⇔= log For example, 29log3= because 932= . Since the irrational number ...71828.2≈e is so important, we write a base e logarithm as ln (“Natural Log”). Properties of Logarithms )(logloglog xzzxbbb=+ =−zxzxbbblogloglog xnxbnbloglog = bxxblnlnlog = ()xeexx==lnln Solve for x. Give exact answers, do not use a calculator. 1.) 164 =x 2.) 81235=+x 3.) ()6ln13=+xe 4.) 532=+xe 5.) 7)53ln(=−x 6.) 3)6(loglog33=++ xx 7.) 0)75ln(2=+− xx 8.) 152=+− xxeeMath 3A -- Prof. Wittman Pre-calc Review: Trigonometric Functions For the diagram at right, the 6 basic trig functions are hypopp=θsin hypadj=θcos adjopp=θtan opphyp=θcsc adjhyp=θsec oppadj=θcot Since the trig functions are periodic, a trigonometric equation often has infinitely many solutions. For example, on the interval ]2,0[π we know that 1sin=x at 2/π=x. If we use the fact that the sine wave repeats every π2 units, we can say that 1sin=x for kxππ22/+= where k is any integer. Solve for x on the interval ]2,0[π. Give exact answers, do not use a calculator. 1.) 3tan7=x 2.) 1sincos32=+ xx 3.) xx cos3cos43= 4.) 03tan2tan2=−− xx Find all values of x which satify the equation below. 5.) 233cos −=−πx 6.)


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UCLA MATH 3A - precalc3A

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