+0

# logarithms pls help

+1
36
2
+59

i got 1/4 but im not sure

Aug 7, 2023

#1
+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 !!!!!

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
+36915
+1

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