Question

$\sf \textsf{What is 'x' in the equation} \ log_2 x + log_4 16 = 2?$

Answer 1

$log_2 x + log_4 16 = 2?$

Refer to attachment :)

Answer 2

Answer:

According to me the answer is 9.

Explanation:

When working with a log equation, the term must be all logs or all numbers.

Change the RHS to a log term as well.

2 log 4  ( x + 7 )  −  log 4  16  =  log 4  16

                           2 = log 4  16

log 4  ( x + 7 ) ^2 − log 4  16 =  log 4  16

We know that, "If logs are being subtracted, the numbers are being divided"

log 4  ( ( x + 7 ) ^ 2 / 16)=  log 4  16

(  x + 7 ) ^2 / 16  =  16

                                    if log A = log B, A = B

(  x + 7 ) ^2  =  256

                                   By cross multiplying....

x + 7 = 16

                                                Only the pos root is valid  and therefore,

x  = 9

Hope this helps you

Hope it is correct

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