The equivalent expression using the properties of logarithms is log2(zx^2/y^2) + log9(y^4x^12)
How to rewrite the expression?
The logarithmic expression is given as:
log2z + 2log2x + 4log9y + 12log9x − 2log2y
Regroup the terms of the expression according to their base
log2z + 2log2x − 2log2y + 4log9y + 12log9x
Rewrite some of the terms as exponents
log2z + log2x^2 − log2y^2 + log9y^4 + log9x^12
Apply the sum and quotient law of indices
log2(z * x^2/y^2) + log9(y^4 * x^12)
Evaluate the products
log2(zx^2/y^2) + log9(y^4x^12)
Hence, the equivalent expression using the properties of logarithms is log2(zx^2/y^2) + log9(y^4x^12)
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