Solve each of the following equations for x. Determine the exact value for x and a decimal approximation correct to four decimals places. 1. 8x−15=0(Solving this equation will locate the x-intercept on the gtaph of y=8x−15) 2. log⁡(x+6)=log⁡(3x−2)+2 (Solving this equation will determine the x-coordinate of the point of intersection of the functions y=log⁡(x+6) and y=log⁡(3x−2)+2.) 3. 4400=2000(1+0.04512)12x (Solving this equation will determine the amount of time it takes an investment $2000 to grow to $4400 if interest is 4.5% compounded monthly.)

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Pohanginah · Accepted Answer

1. 8x−15=0  8x=15  Take ln both side  ln⁡8x=ln⁡15  Using, ln⁡ab=bln⁡a  xln⁡8=ln⁡15  x=ln⁡15ln⁡8  x=1.3023  2. log⁡(x+b)=log⁡(3x−2)+2  log⁡(x+6)−log⁡(3x−2)=2  Using, log⁡a−log⁡b=log⁡(ab)  log⁡(x+63x−2)=2  Using, log⁡a=b  then a=10b  x+63x−2=102  x+6=(3x−2)×100  x+6=300x−200  300x−x=200+6  299x=206  x=206299  x=0.6889  3. 4400=2000(1+0.04512)  44002000=(12+0.04512)12x  2.2=(1.0038)12x  Take ln both side  ln⁡2.2=ln⁡(1.0038)12x  ln⁡(2.2)=12xln⁡(1.0038)  x=ln⁡2.212ln⁡1.0038  x=17.3236.

Solve each of the following equations for x. Determine the exact value for x and

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