What is the true solution to the logarithmic equation below

Asked by maham237 @ 20/05/2021 in Mathematics viewed by 447 People

log4[log4(2x]=1
x=2
x=8
x=65
x=128

Answered by maham237 @ 20/05/2021

1.
write 1 as $log_{4}4$ so that we compare same base logarithms:

$log_{4}[{ log_{4}}2x]= log_{4}4$

2. Neglect the equal bases and write the arguments:

So ${ log_{4}}2x=4$

repeat step 1, that is write 4 as a logarithm with base 4:

$4=4*1=4* log_{4}4= log_{4} 4^{4}$

3. ${ log_{4}}2x=log_{4} 4^{4}$

$2x=4^{4}$

$x= \frac{4^{4}}{2}= 4^{3}*2=64*2=128$

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