Question

Solve 2^(x-1) =11 change of base

Answer 1

x = 4.46

Explanation:

We are to solve the following expression:

`2^((x-1))=11`

Taking the natural logarithm of both sides of the equation to remove the variable from the exponent. to get:

`ln ( 2 ^ { x - 1 } ) = l n ( 1 1 )`

`( x - 1 ) l n ( 2 ) = l n ( 1 1 )`

Applying the distributive property:

`xln(2)-1ln(2)=ln(11)`

Solving for x to get:

`x=(ln(11))/(ln(2)) +1`

x = 4.46

Answer 2

`x=4.459`

Explanation:

We have the following equation

`2^((x-1)) =11`

To solve the function, apply the equation
`log_2` on both sides of the equation

`log_2(2^((x-1))) =log_2(11)`

Remember that

`log_b(b)^x =x`

So

`(x-1) =log_2(11)`

`x =log_2(11) + 1`

Finally

`x=4.459`