# How do you solve -\log 8= 3- \log x?

May 13, 2017

Isolate $\log x$ then use the definition of a logarithm to solve for $x$. Answer: $8000$

#### Explanation:

Question: $- \log 8 = 3 - \log x$

Note that $\log \left(x\right)$ is the same as ${\log}_{10} \left(x\right)$

We can see that $- \log 8$ and $3$ are both constants, so we move them to one side and make $\log x$ positive:
$\log x = 3 + \log 8$

Now we can use the definition of a logarithm (${\log}_{b} a = c \to {b}^{c} = a$) to take $x$ out of the log:
$x = {10}^{3 + \log 8}$

$= {10}^{3} \cdot {10}^{\log 8}$

Since, exponential and logarithmic are inverse functions, they cancel each other:
$= 1000 \cdot 8$

$= 8000$