SOLUTION: if log a=2 and log b=3, what is the numerical value of log square root a / b^3 ?

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Question 389942: if log a=2 and log b=3, what is the numerical value of
log square root a / b^3 ?

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

Since you're given log(a) and log(b), this expression can be evaluated if we can rewrite this expression in terms of log(a) and/or log(b). To do this we start by using the property of logarithms, , to write the logarithm of a quotient as the difference of the logarithms of the numerator and denominator:

Since square roots are the same as an exponent of 1/2 this can be written as:

Next we can use another property of logarithms, , to move the exponents in the arguments out in front:

We now have the expression in terms of log(a) and log(b). We can substitute in their values:

which simplifies as follows:
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