Question

Solve 6x + 2 = 10 for x using the change of base formula log base b of y equals log y over log b.

Answer 1

x= -0.715

Explanation:

6^x+2 = 10

Step 1: Apply ln rule on both sides

ln rule: x^y = z

ln rule: (y)ln(x) = ln(z)

6^x+2 = 10

(x+2)*ln(6) = ln(10)

(x+2) = ln(10)/ln(6)

x+2 = 1.285

x = -0.715

Therefore, the right answer is the second option -0.715

!!

Answer 2

The answer is -0.715

Explanation:

Firstly, we use the change of base formula. The base must be 6 because the "x" variable is a power of it.

`6^x^+^2=10\\\\log_(6) (6^x^+^2)=log_(6) (10)\\`

Then, we can use the property logarithm power rule:

`log_(b)(x^y)=y* log_(b)(x)`

So,

`(x+2)*log_(6) (6)=log_(6) (10)\\log_(6) (6)=1\\x+2=log_(6) (10)\\\\log_(6) (10)=(log(10))/(log(6))\\log(10)=1\\\\x+2=(1)/(log(6)) \\x=(1)/(log(6))-2`

Finally, the value of
`(1)/(log(6)) =1.285`, therefore:

`x=1.285-2=-0.715`