Solved given expression for x using the change of base formula log base b of y equals log y over log b is 4.459
Answer: Option D
Step-by-step explanation:
Given Expression:
[tex]2^{x-1}=11[/tex]
To solve this, first convert the exponential form into log form
If [tex]a^{x}=b[/tex] then [tex]\log _{a}(b)=x[/tex]
So, when comparing the given expression with above, a = 2, x = x – 1 and b = 11
.
[tex]2^{x-1}=11[/tex] become [tex]\log _{2}(11)=x-1[/tex]
Now, apply change of base formula to remove base 3
[tex]\log _{a}(y)=\frac{\log y}{\log a}[/tex]
Hence,
[tex]\log _{2}(11)=\frac{\log 11}{\log 2}[/tex]
Substitute [tex]\log _{2}(11)=x-1[/tex] in above expression, we get
[tex]\frac{\log 11}{\log 2}=x-1[/tex]
[tex]\frac{1.0414}{0.301}=x-1[/tex]
x – 1 = 3.459
x = 3.459 + 1 = 4.459
