I think your equation is [tex]2^{x-1} = 11[/tex]
Answer:
[tex]x=4.459[/tex]
Step-by-step explanation:
To solve the equation take natural log on both sides of equation:
[tex](x-1)ln(2)=ln(11)[/tex] (∵ [tex]log(a^{b} )= b \times log(a)[/tex] )
[tex]x - 1=ln(11)/ln(2)[/tex]
(remember [tex]ln[/tex] and [tex]log_{e}[/tex] are same)
using base changing property:
[tex]x-1=log_{2} (11)[/tex] (∵ [tex]\frac{log_{e}(11) }{log_{e}(2)} = log_{2}(11)[/tex])
[tex]x=log_{2}(11)+1[/tex]
[tex]x=4.459[/tex]
