# How do you solve #log_2 x + log_4 x + log_8 x + log_16 x = 25#?

##### 2 Answers

Solution

#### Explanation:

We can start by converting all of the

Now we can pull

Notice that all of the denominators are powers of 2, so we can rewrite as;

Using the identity,

Now we can pull

We can rewrite all of the fractions in term of the lowest denominator.

Sum the terms in parenthesis.

We can combine all of the constant terms by multiplying both sides by the inverse of the fraction on the left hand side.

Combine the

Using the definition of a logarithm, we write this statement in terms of

Solve.