Question

Express in terms of logarithms without exponents log_c(x^9y^9z) What is the equivalent expression?

Answer 1

Step-by-step explanation:

We have to use two properties of logarithms:

Logarithm of a product:

`\log _a(x\cdot y)=\log _a(x)+\log _a(y)`

Logarithm of a power:

`\log _a(x^b)=b\cdot\log _a(x)`

For this problem:

`\log _c(x^(9)y^(9)z)`

First we solve the logarithm of a product part:

`\log _c(x^9y^9z)=\log _c(x^9)+\log _c(y^9)+\log _c(z)`

And then, the logarithm of a power part:

`\log _c(x^9y^9z)=9\log _c(x^{})+9\log _c(y^{})+\log _c(z)`

Answer:

`\log _c(x^9y^9z)=9\log _c(x^{})+9\log _c(y^{})+\log _c(z)`