Question

Solve 2x − 1 = 11 for x using the change of base formula log base b of y equals log y over log b.

Answer 1

I think your equation is $2^{x-1} = 11$

Answer:

$x=4.459$

Step-by-step explanation:

To solve the equation take natural log on both sides of equation:

$(x-1)ln(2)=ln(11)$         (∵  $log(a^{b} )= b \times log(a)$ )

$x - 1=ln(11)/ln(2)$

(remember $ln$ and $log_{e}$ are same)

using base changing property:

$x-1=log_{2} (11)$       (∵ $\frac{log_{e}(11) }{log_{e}(2)} = log_{2}(11)$)

$x=log_{2}(11)+1$

$x=4.459$