UNIT 5 WORKSHEET 9 Exponential and Logarithmic Equations 1 Solve each of the following.(Round answers to 3 decimal places) 1) 3^2x-4=5 2) 3^5x+6=4^x 3) 5^2x-4=3^4x-5 4) (1+(0.10)/(12))^12t=2 5) lnx+ln(x-2)=1 6) e^2x=7 7) 2-6ln3x=10 8) log_(2)x+log_(2)(x+2)=log_(2)(x+6) 9) e^2x+3e^x-10=0

Let's solve each of the given exponential and logarithmic equations step by step.<br /><br />1) $3^{2x-4}=5$<br /> Taking the logarithm of both sides:<br /> $\log(3^{2x-4})=\log(5)$<br /> $(2x-4)\log(3)=\log(5)$<br /> $2x-4=\frac{\log(5)}{\log(3)}$<br /> $2x=\frac{\log(5)}{\log(3)}+4$<br /> $x=\frac{1}{2}\left(\frac{\log(5)}{\log(3)}+4\right)$<br /> $x\approx 1.464$<br /><br />2) $3^{5x+6}=4^{x}$<br /> Taking the logarithm of both sides:<br /> $\log(3^{5x+6})=\log(4^{x})$<br /> $(5x+6)\log(3)=x\log(4)$<br /> $5x+6=\frac{x\log(4)}{\log(3)}$<br /> $5x-\frac{x\log(4)}{\log(3)}=-6$<br /> $x\left(5-\frac{\log(4)}{\log(3)}\right)=-6$<br /> $x=\frac{-6}{5-\frac{\log(4)}{\log(3)}}$<br /> $x\approx 0.462$<br /><br />3) $5^{2x-4}=3^{4x-5}$<br /> Taking the logarithm of both sides:<br /> $\log(5^{2x-4})=\log(3^{4x-5})$<br /> $(2x-4)\log(5)=(4x-5)\log(3)$<br /> $2x-4=\frac{(4x-5)\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)}{\log(5)}-\frac{5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)}{\log(5)}-\frac{5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-5\log(3)}{\log(5)}$<br /> $2x-4=\frac{4x\log(3)-