Question 432469

your answer is correct...:-)

here is my version too:

—The Relationship—    
    
  {{{y = bx}}} 	

 
..............is equivalent to...............(means the exact same thing as)
	

{{{logb(y) = x  }}}


Change from exponential form to logarithmic form and solve for {{{x}}}:

{{{3^(x-2)=7}}}

A)solve for {{{x }}}(exact solution)
B)use calculator to solve for {{{x}}} and round to nearest thousandth 

  {{{y = bx}}} ...................{{{logb(y) = x }}} 

{{{y=3^(x-2)-7}}}.............

{{{y=3^(x-2)-7}}}............ {{{log(3^(x-2)) = 7}}}

  		    {{{(x-2)ln(3) = ln7 }}} 

  		     {{{x-2 = ln7/ ln(3)}}}

 {{{x = ln7/  ln(3) +2}}}

 {{{x = 1.9459/  1.099 +2}}}

 {{{x = 1.9459/  1.099 +2=1.7706+2=3.771}}}

{{{3^3.771-2=7}}}

{{{3^1.771=7}}}

{{{6.998=7}}}

{{{7=7}}}