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if \(\log_{10}(x) = 3 + \log_{10}(y)\), find \(\dfrac{x}{y}\).

 

Let x and b be positive real numbers so that \(\log_b(x^2) = 10\) Find \(\log_{\sqrt[3]{b}} \left( \frac{1}{x} \right)\)

 

so i've been stuck on these problems.... im pretty sure we apply some log formula to it but im not sure what.

 

help appreciated!

 

thank you!!

 Mar 28, 2022
 #1
avatar+36434 
+2

log x - log y = 3

 

log (x/y) = 3

x/y = 103 = 1000

 Mar 28, 2022
 #2
avatar+36434 
+2

I think this is how to do this one:

 

logb (x^2) = 10

2 logb (x) = 10

logb (x) = 5

 

Now use the log base-change rule for the second part   ( to change to base 'b' )

 

    = logb (1/x) / logb ( b1/3

    = logb (x-1) / ( 1/3 logb (b) )              remember   logb (b) = 1

   = (-1) logb (x) / (1/3)

   = -3 logb(x)   = - 3 ( 5) = -15  

ElectricPavlov  Mar 29, 2022
 #3
avatar+117849 
+1

Nice going EP.

I got the same answers.

Melody  Mar 29, 2022
 #4
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+1

i actually asked my teacher about this one and she said the exact same thing!! thanks for the help!!

Guest Mar 30, 2022

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