What is x for: `log_2 7 + log_2 3 = log_2 x`

Expert Answers
justaguide eNotes educator| Certified Educator

The value of x has to be determined for `log_2 7 + log_2 3 = log_2 x`

Use the property of logarithms `log a + log b = log (a*b)` for all the log having the same base.

`log_2 7 + log_2 3 = log_2 x`

=> `log_2 (7*3) = log_2 x`

=> `log_2 21 = log_2 x`

=> x = 21

The value of x = 21

joshuakl | Student

logsubscript2 (7)+logsubscript2(3)=log subscript2 is the same as

logsubscript2 (3x7) = log subscript2 (Blank).

Take both sides to this: 2^logsubscript2 (21) = 2^logsubscript2 (blank). The 2 and logsubscript2 cancel out to give you

21 = blank

For the second use the same principle just divide the subtracted logarithms and for the last one 2 is taken to the power of blank and do the same thing to solve the equation as you did in the first example. Hope this helps!

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