Solving for the value inside a base 10 logarithm

Question

I have an equation of $\log(d)=(-x-A)/(10n)$ that I need to solve for $d$. How do I "reverse" the logarithm to obtain $d$? I apologize if this is super easy, I just can't even figure out how to Google it!

Answer 1

If $\log_{10} d=f$ you can raise $10$ to the power of each side, getting $10^{\log_{10} d}=d=10^f$, where the first equality is the definition of the logarithm.

Answer 2

Remember what logarithms are: They're the inverse of exponents. A base 10 logarithm is the inverse of 10 raised to a power. So to get $d$ out of the log, you can do so by using both sides of the equation as an exponent of 10.

$10^{\log{d}} = 10^{(-x - A)/(10n)}$

and $10^{\log{d}} = d$.

Answer 3

You can re write the expression as $10n \cdot log_{10} d=-x-A$

or, $$d^{10n}=\frac{1}{10^{x+A}}$$

can you take it from here?