What are the values of h and k ?

Given that #log_2 hk = 3# and #log_2 h^3 k^2 = 5# , find the values of h and k.

Answer 1

#h=1/2, k=16#

One method is as follows:

applying the log's laws

#log_ab=c=>a^c=b#
#log_aX+log_aY=log_a(XY)#
#log_aX^n=nlog_aY#
#-----------------#
#log_2(hk)=3=>color(red)(log_2h+log_2k=3--(1))#
#log_2(h^3k^2)=5#
#=>log_2h^3+log_2k^2=5#
#=>color(blue)(3log_2h+2log_2k=5---(2))#
#xx(1) " "by" " 2#
#color(red)(2log_2h+2log_2k=6--(1))#
#color(blue)(3log_2h+2log_2k=5---(2))#

Subtract

#-log_2h=1#
#=>log_2h=-1=>h=1/2#
substitute back into #(1)#
#log_2h+log_2k=3--(1))#

gives

#-1+log_2k=3#
#=>log_2k=4#
#=>k=2^4=16#
so #h=1/2, k=16#

Verifying the consistency of the second equation

3log_2h + 2log_2k = 5

#LHS" "3xx-1+2xx4=-3+8=5=RHS#
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Answer 2

To determine the values of ( h ) and ( k ), we need additional information or context. It seems like you might be referring to a specific mathematical problem or equation where ( h ) and ( k ) represent variables or parameters. Could you provide more details or specify the equation or problem you're referring to? With more information, I can assist you in finding the values of ( h ) and ( k ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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