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here were asked to evaluate a logarithm given certain facts okay so the first step is to expand this logarithm and then well plug in the values so the first thing I notice is this multiplication lets expand this as addition log base B of A plus log base B of the cubed root of C squared now to expand this further we have to rewrite this radical as an exponent so log base B of A plus log base B of C now written as a rata as a fractional exponent that radical would be to the two-thirds power remember the numerators the power and the denominators the root written as a power we can use the property of exponents that says exponent the property of logarithms that says exponents can be written as coefficients so then we would have log base B of A plus two-thirds times log base B of C now were ready to plug in the appropriate values log base B of A was given to be negative 1 so lets plug that in there plus two-thirds times log base B of C which was given to be 9 okay so working it out wed