Question

Write the following expression as a sum and/or difference of logarithms. Express exponents as factors:

log5[x^2z^9w√x^4-81]

Answer 1

log5[x^2z^9w√(x^4-81)]

Using the properties of logarithms, we can rewrite the given expression as a sum and/or difference of logarithms as follows:

log5[x^2z^9w√(x^4-81)] = 2log5(x) + 9log5(z) + log5(w) + 0.5log5(x^4-81)

Note that the square root (√) can be expressed as a exponent of 0.5, and we can use the properties of logarithms to split the logarithm of a product into a sum of logarithms of individual factors.

Explanation: