# How do you write log_14 196=2 in exponential form?

Jul 27, 2016

${14}^{2} = 196$

#### Explanation:

Suppose you had ${\log}_{a} x = y$

They would call this log to base $a$

Then it means: ${a}^{y} = x$ .............................Equation(1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that ${\log}_{a} \left(a\right) = 1$

So:
${\log}_{2} \left(2\right) = 1 \text{ "->" } {2}^{1} = 2$
${\log}_{10} \left(10\right) = 1 \text{ "->" } {10}^{1} = 10$
${\log}_{e} \left(e\right) = 1 \text{ "->" } {e}^{1} = e$

$L o {g}_{e}$ is a special one case.

You normally see this written as $\ln$

So you could have $\ln \left(x\right)$ sometimes you see it as $\exp \left(x\right)$

The last one is quite often used in computer software and in higher maths.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that ${\log}_{10} \left(1\right) = 0$ as is any ${\log}_{x} \left(1\right) = 0$

Look at Equation(1) and you will observe that

as in ${\log}_{a} x = y \text{ "->" } {a}^{y} = x$

$\text{ "log_10(1)=0" "->" } {10}^{0} = 1$

Any value (apart from 0) raised to the power of 0 has the value 1

Consider: ${x}^{z} / {x}^{z} = 1$ this is the same as ${x}^{z - z} = {x}^{0} = 1$

Jul 27, 2016

${\log}_{14} 196 = 2 \text{ " rArr " } {14}^{2} = 196$

#### Explanation:

Changing from log from to index form can be done by purely following the definition.

${\log}_{a} b = c \text{ " rArr } {a}^{c} = b$

Remember:
"The base stays the base and the other two change around"

${\log}_{14} 196 = 2 \text{ " rArr " } {14}^{2} = 196$