Question

Solve the given inequality. If necessary, round to four decimal places.13^4a < 19

Answer 1

Answer:

The solution of the inequality is a < 0.2870

Step-by-step explanation:

* Lets talk about the exponential function

- the exponential function is f(x) = ab^x , where b is a constant and x

 is a variable

- To solve this equation use ㏒ or ㏑

- The important rule ㏒(a^n) = n ㏒(a) OR ㏑(a^n) = n ㏑(a)

* Lets solve the problem

∵ 13^4a < 19

- To solve this inequality insert ㏑ in both sides of inequality

∴ ㏑(13^4a) < ㏑(19)

∵ ㏑(a^n) = n ㏑(a)

∴ 4a ㏑(13) < ㏑(19)

- Divide both sides by ㏑(13)

∴ 4a < ㏑(19)/㏑(13)

- To find the value of a divide both sides by 4

∴ a < [㏑(19)/㏑(13)] ÷ 4

∴ a < 0.2870

* The solution of the inequality is a < 0.2870

Answer 2

Answer:

a < 0.2870

Step-by-step explanation:

We are given the following inequality which we are to solve, rounding it to four decimal places:

$1 3 ^ { 4 a } < 1 9$

To solve this, we will apply the following exponent rule:

$a = b ^ { l o g _ b ( a ) }$

$19=13^{log_{13}(19)}$

Changing it back to an inequality:

$13^{4a}$

If $a > 1$ then $a^{f(x)}$ is equivalent to $f(x)}< g(x)$.

Here, $a=13$, $f(x)=4a$ and $g(x)= log_{13}(19)$.

$4a$

$a$

a < 0.2870