# arrow_back How do you evaluate a logarithm?

82 views
How do you evaluate a logarithm?

Many logarithms may be calculated by converting them to exponential form. Suppose we want to calculate the value of $\log _{2}(16)$. Start by writing this expression as a logarithmic form,
$\log _{2}(16)=?$
We could write the output with a variable, but a question mark suffices to indicate what we want to find. If we convert this form to an exponential form with a base of 2 ,
$2^{?}=16$
The left-hand side may be written with the base 2 as $2^{4}$. Substitute this expression in place of 16
$2^{?}=2^{4}$
Since the exponent on the left side must be 4, this is also the value in the original exponential form,
$\log _{2}(16)=4$
by Bronze Status
(7,476 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
How do you evaluate $\lim_{x \rightarrow 0} {\dfrac{\sqrt{4+x} - 2} {3x}}$
How do you evaluate $\lim_{x \rightarrow 0} {\dfrac{\sqrt{4+x} - 2} {3x}}$How do you evaluate $\lim_{x \rightarrow 0} {\dfrac{\sqrt{4+x} - 2} {3x}}$ ...
close
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
How do you solve $\dfrac{1}{2\sqrt{2x-5}-1}{2\sqrt{3x+4}}=-1$?
How do you solve $\dfrac{1}{2\sqrt{2x-5}-1}{2\sqrt{3x+4}}=-1$?How do you solve $\dfrac{1}{2\sqrt{2x-5 }-1}\cdot{2\sqrt{3x+4}}=-1$? ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\sqrt{x^{2}+y^{2}+1}=?$
Evaluate $\sqrt{x^{2}+y^{2}+1}=?$\begin{aligned} &amp;x^{2}=17 x+y \\ &amp;y^{2}=x+17 y \\ &amp;x \neq y \\ &amp;\sqrt{x^{2}+y^{2}+1}=? \end{aligned} ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate this Limit Using Simplification
Evaluate this Limit Using SimplificationEvaluate this Limit Using Simplification $$\lim _{x \rightarrow-2} \frac{3 x^{2}+x-10}{x+2}$$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\lim _{x \rightarrow 1}\left(\frac{y-4 \sqrt{y}+3}{y^{2}-1}\right)$
Evaluate $\lim _{x \rightarrow 1}\left(\frac{y-4 \sqrt{y}+3}{y^{2}-1}\right)$Evaluate $\lim _{x \rightarrow 1}\left(\frac{y-4 \sqrt{y}+3}{y^{2}-1}\right)$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\lim _{x \rightarrow-4} \frac{x^{2}-16}{x+4} \ln |x|$
Evaluate $\lim _{x \rightarrow-4} \frac{x^{2}-16}{x+4} \ln |x|$Evaluate $\lim _{x \rightarrow-4} \frac{x^{2}-16}{x+4} \ln |x|$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\lim _{x \rightarrow 10} \sqrt{-x^{2}+20 x-100}$
Evaluate $\lim _{x \rightarrow 10} \sqrt{-x^{2}+20 x-100}$Evaluate $\lim _{x \rightarrow 10} \sqrt{-x^{2}+20 x-100}$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\lim _{x \rightarrow 10} f(x)$, where $f(x)=x^{2}$ for all $x \neq 10$, but $f(10)=99 .$
Evaluate $\lim _{x \rightarrow 10} f(x)$, where $f(x)=x^{2}$ for all $x \neq 10$, but $f(10)=99 .$Evaluate $\lim _{x \rightarrow 10} f(x)$, where $f(x)=x^{2}$ for all $x \neq 10$, but $f(10)=99 .$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\lim _{x \rightarrow 10} \frac{x^{2}-100}{x-9}$
Evaluate $\lim _{x \rightarrow 10} \frac{x^{2}-100}{x-9}$Evaluate $\lim _{x \rightarrow 10} \frac{x^{2}-100}{x-9}$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\lim _{x \rightarrow 10} \frac{x^{2}-99}{x-10}$
Evaluate $\lim _{x \rightarrow 10} \frac{x^{2}-99}{x-10}$Evaluate $\lim _{x \rightarrow 10} \frac{x^{2}-99}{x-10}$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\lim _{x \rightarrow \infty}\left(\frac{2 x^{2}-2 x-3}{x^{2}-1}\right)$
Evaluate $\lim _{x \rightarrow \infty}\left(\frac{2 x^{2}-2 x-3}{x^{2}-1}\right)$Evaluate $\lim _{x \rightarrow \infty}\left(\frac{2 x^{2}-2 x-3}{x^{2}-1}\right)$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\lim_{x \rightarrow -\infty}\dfrac{1}{2x^3}$
Evaluate $\lim_{x \rightarrow -\infty}\dfrac{1}{2x^3}$Evaluate $\lim_{x \rightarrow -\infty}\dfrac{1}{2x^3}$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate $\lim_{x \to \infty } \left ( \frac{2x^{2}-2x-3}{x^{2}-1} \right )$
Evaluate $\lim_{x \to \infty } \left ( \frac{2x^{2}-2x-3}{x^{2}-1} \right )$Evaluate $\lim_{x \to \infty } \left ( \frac{2x^{2}-2x-3}{x^{2}-1} \right )$ ...
Evaluate the limit $\lim_{x\rightarrow 0}{(e^x+3x)}^{\dfrac{1}{x}}$?
Evaluate the limit $\lim_{x\rightarrow 0}{(e^x+3x)}^{\dfrac{1}{x}}$?Evaluate the limit $\lim_{x\rightarrow 0}{(e^x+3x)}^{\dfrac{1}{x}}$? ...