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!!
+36915 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
