Question

In the following exercise, solve for x.

$\log 49=2\log x$

Short answer

The solution of the given expression is $x=7$

Step-by-step solution

. Given information.

The given expression is$\log 49=2\log x$$\log 49=2\log x$

Step 2. Use logarithmic properties 

Using power property, we get:

$$\begin{gathered} \log 49=2\log x \\ \log 49=\log x^2 \end{gathered}$$

Using one to one property, we get:

$$\begin{gathered} \log 49=\log x^2 \\ 49=x^2 \\ {x}^2=49 \end{gathered}$$

Step 3. Solve for x.  

Solving the equation, we get:

$$\begin{gathered} x^2=49 \\ x=\pm \sqrt{49}[rootingbothsides] \\ x=\pm 7 \end{gathered}$$

We can eliminate $x=-7$because the logarithmic function doesn't take negative values.

Step 4. Check the values 

Substituting $x=7$in the given expression, we get:

$$\begin{gathered} \log 49=2\log x \\ \log 49=2\log 7 \\ \log 49=\log 7^2 \\ \log 49=\log 49 \end{gathered}$$

This is True.

Thus $x=7$is the solution of the given function.