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# if , find .

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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
+36416
+2

log x - log y = 3

log (x/y) = 3

x/y = 103 = 1000

Mar 28, 2022
#2
+36416
+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
+117105
+1

Nice going EP.