+0  
 
+1
36
2
avatar+59 

i got 1/4 but im not sure

thx in advance

 Aug 7, 2023
 #1
avatar+128408 
+1

log √3 3^4 = logx 4

 

4 log √3 3 =  log x 4

 

4 log √3 (√3)^2  = log x  4       

 

(2 * 4 )  log √3 (√3)   = log x 4              (    log √3 (√3) =  1)

 

2 * 4 * 1    = log x  4

 

8  = log x  4           (x must be positive)

 

This means that    x^8 = 4    →   take the positive 8th root of both sides....

 

x  = 4^(1/8) =  (2^2)^(1/8) = 2^(1/4)

 

So

 

log 2  x  =   log 2 2 ^(1/4)  =    (1/4) log 2 2    = (1/4) * 1  = 1/4

 

And you are  correct !!!!!

 

 

 

cool cool cool

 Aug 7, 2023
edited by CPhill  Aug 7, 2023
edited by CPhill  Aug 7, 2023
edited by CPhill  Aug 7, 2023
edited by CPhill  Aug 7, 2023
 #2
avatar+36915 
+1

Start with the LEFT side 

      Using the definition of logs :   (  31/2  ) = 34      shows  n = 8       ( or you can just use a calculator to find the L side = 8) 

                   so the left side = 8 

8 = log4

                             

since y = log2 x    then  2y = x     ( using definition of logs) 

 

then     8 = log 2y  4   

       ( 2y )8   = 4                   (using definition of logs again) 

           28y = 22                        (equate the exponents) 

               8y = 2 

               y = 1/4 

 Aug 7, 2023

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