Solve 4^x-5 = 6 for x using the change of base formula log base b of y equals log y over log b

Answer:[tex]4^x-5=6[/tex] gives the solution [tex]x=\frac{\log(11)}{\log(4)}[/tex].[tex]4^{x-5}=6[/tex] gives the solution [tex]x=\frac{\log(6)}{\log(4)}+5[/tex].Step-by-step explanation:I will solve both interpretations.If we assume the equation is [tex]4^{x}-5=6[/tex], then the following is the process:[tex]4^x-5=6[/tex]Add 5 on both sides:[tex]4^x=6+5[/tex]Simplify:[tex]4^x=11[/tex]Now write an equivalent logarithm form:[tex]\log_4(11)=x[/tex][tex]x=\log_4(11)[/tex]Now using the change of base:[tex]x=\frac{\log(11)}{\log(4)}[/tex].If we assume the equation is [tex]4^{x-5}=6[/tex], then we use the following process:[tex]4^{x-5}=6[/tex]Write an equivalent logarithm form:[tex]\log_4(6)=x-5[/tex][tex]x-5=\log_4(6)[/tex]Add 5 on both sides:[tex]x=\log_4(6)+5[/tex]Use change of base formula:[tex]x=\frac{\log(6)}{\log(4)}+5[/tex]