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Let log base 4 of 3 = x. Then log base 8 of 27 = kx. Find k.

 Nov 30, 2020
 #1
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k =2

 Nov 30, 2020
 #2
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log 4 3  = x      log 8 27  = kx

 

Put  these in exponential form

 

4x  = 3          8kx  = 27

 

(22)x =  3       (23)kx  = 27

 

(22x)  = 3      (22x) 1.5k = 27

 

                      (3)1.5k  = 27

 

                      (3)1.5k = 33

 

Solve for the exponents

 

1.5k =  3

 

k  = 2

 

 

cool cool cool

 Nov 30, 2020
 #3
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+1

Flip 'em to base 10     log 3/ log 4 = x

 

log 27 /log8 = kx = k log3/log4

k = log27/log8 * log4/log3 = 2

 Nov 30, 2020

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