SOLUTION: express logarithm of log base c 5= a and log base c 4 =b find log base c of 2 and log base c of 10

Question 286328: express logarithm of log base c 5= a and log base c 4 =b
find log base c of 2
and log base c of 10
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

To find we will need to use the properties on the base c logarithms we have. There are properties for products, quotients and powers of arguments. Since 4 is a power of 2 we can use and the property about powers in the argument of a logarithm to find :

Using the property, , to move the exponent out of the argument:

Now we jsut divide by two:

We now have three base c logarithms. For we look for a product, quotient or power of 2, 4 and/or 5 which makes 10. Obviously 2*5=10 so:

Now we can use the property for products in an argument, , to separate the 2 and the 5:

We can replace these logarithms with what we know them to be:

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