Exponential and Logarithmic Equations solve the equation. Find the exact solution if possible. otherwise, use a calculator to approximate to two decimals. logx(x+5)−log8(x−2)=1

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Exponential and Logarithmic Equations solve the equation. Find the exact solution if possible. otherwise, use a calculator to approximate to two decimals.  logx(x+5)−log8(x−2)=1

Macsen Nixon · Accepted Answer

Step 1  Law of logarithm:  Consider m to be a positive number and m≠q1.  Again consider M and M to be any real numbers with M&amp;gt;0 and N&amp;gt;0.  The difference of logarithms of two numbers is equal to the logarithm of quotient of two numbers as,  logmM−logmN=logm(MN)  The logarithm function with base m is denoted by logm can be defined as,  logmM=y  M=my  Step 2  The given logarithm equation is,  1) log8(x+5)−log8(x−2)=1  The above logarithm equation can be combined from the laws of logarithm as,  2) log8(x+5)(x−2)=1  The equation (2) can be expressed as,  (x+5)(x−2)=81  x+5=8(x−2)  x+5=8x−16  x−8x=−16−5  Simplify above equation as,  −7x=−21  7x=21  x=217  x=3  Therefore, x=3 is the solution of equation log8(x+5)−log8(x−2)=1.  Conclusion:  Thus, the solution of the logarithm equation log8(x+5)−log8(x−2)=1 is 3.

Find the exact solution if possible. otherwise, use a calculator to approximate to two decimals \log_{x}(x+5)-\log_{8}(x-2)=1

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