Replace the variables a and b with integers and solve for log a b = x by using the change of base formula. Show all work and use complete sentences to explain your steps in solving the logarithm you created.

Question

zepp · Answer

Let's say a = a and b = b

zepp · Answer

And $\large \log_ab=x$
Rewrite is in exponential form.
$\large a^x = b$
Take the log of the both side
$\large log_ax= \log b$

By using a log property
$\large x log_a = log_b$
Divide by log a to both side
$\large x = \frac{\log b}{\log a}$

dumbcow · Answer

$$\log_{a} b = \frac{\log b}{\log a}$$

zepp · Answer

Therefore, the equation @dumbcow typed.

anonymous · Answer

but dont i need numbers instead of variables?

dumbcow · Answer

yes , @zepp showed the derivation of where the change of base formula came from

zepp · Answer

The property may not be very clear but there's a hidden base.

zepp · Answer

That's why I can apply the property.

zepp · Answer

Arrgh, I lost everything I just typed :(

zepp · Answer

$\huge \begin {align}
a^x&=b \
log_{10}a^x &= log_{10}b \
xlog_{10}a&=log_{10}b \
x &= \frac{\log_{10}b}{log_{10}a}
\end {align}$

There, we can ignore the base, but that's just to show the invisible base there.

anonymous · Answer

thanks