algebra 2 problem

Question

Log₄ (x+7)=2     ??????

Answer 1

log₄ (x + 7) = 2             convert to exponential form

4² = x + 7                     square

16 = x + 7                     subtract 7 from both sides

9 = x

 

Check

log₄ (9 + 7) = 2

log₄ 16 = 2

2 = 2

Answer 2

Hi Diane, here is how:

 

log₄ ( x + 7 )  =  2

 

b^log_bx = x   (inverse property for logarithm)

 

Use that inverse property.

 

4^{log₄ ( x+ 7 )}  =  4²     (exponentiate both side with 4)

 

* In this process, 4^log₄ cancels out.

 

( x + 7 )   =  16

 

x = 9

 

 

Let's check it:

 

log₄ (x + 7) = 2

log4 (9 + 7) = 2

log₄   (16)   = 2

log₄ 4²        = 2           4² = 4²

(Property of Logarithm)  (log and 4s (the base) are canceling out)

   2        =       2

 

 

Good luck to you.

 

Yohan Chu   (LV  NV)