Question

Expand each logarithm. log₃[(xy 1/3)+z²]³

Answer 1

After expanding logarithm equation is : $3.log_3(xy^\frac{1}{3} + z^2)$

What is logarithmic equation ?

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   $log_ax=N$

where, a is the base of function or equation

           x define expression

Mathematically, if  $a^N=x$  is an exponential function then, this can be converted to logarithmic function as  $log_ax=N$.

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

• log_c a × b = log_c a + log_c b  , c is the base
• log a/b = log a - log b
• log a^x = x log a
• log a^a = 1
• log (√x) = 1/2 log (x)

The given expression can be written as,

$log_3[xy^\frac{1}{3} + z^2]^3$

apply formulas log a^x = x log a

=> $3.log_3(xy^\frac{1}{3} + z^2)$

Thus, after expanding the logarithm equation is : $3.log_3(xy^\frac{1}{3} + z^2)$

To know more about logarithms, visit :

brainly.com/question/5956809

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