Calculate the power of that makes the expression equal to 25. We can set up an alternate or equivalent equation to solve this problem:

Solve this equation by taking the square root of both sides.

, because logarithmic equations cannot have a negative base.

The solution to this expression is:

Given log4_x_ = 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.

Here, we need to make use of some logarithm identities:

Therefore, putting all of those things together, we get the final answer of

Using the property that , we can simplify the expression to .

Given that and

We can further simplify this equation to

You can change the form to

3_x_ = 27

x = 3

Use the following equation to easily manipulate all similar logs:

changes to .

Therefore, changes to .

2 raised to the power of 6 yields 64, so must equal 6. If finding the 6 was difficult from the formula, simply keep multiplying 2 by itself until you reach 64.

Since the two logarithmic expressions on the left side of the equation have the same base, you can use the quotient rule to re-express them as the following:

log224 – log23 = log2(24/3) = log28 = 3

Therefore we have the following equivalent expressions, from which it can be deduced that x = 3.

log_x_27 = 3

_x_3 = 27

To solve, we use logarithms. We log both sides and get: log3 = log2x

which can be rewritten as log3 = xlog2

Then we solve for x: x = log 3/log 2 = 1.5850 . . .

To solve an exponential equation like this, you need to use logarithms. This can be translated into:

Now, remember that your calculator needs to have this translated. The logarithm is equal to the following:

, which equals approximately .

Remember that you have the equation:

Thus, .

In order to solve a question like this, you will need to use logarithms. First, start by converting this into a basic logarithm:

Recall that you need to convert for your calculator:

, which equals approximately

Thus, you can solve for :