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2 years ago

243^0.2x=81^x+5Could you please help me with the steps to this problem?

1 answer:

3 0

Answer:

-20/3

Step-by-step explanation:

First simplify the left side of the equation

243^(1/5x)= (243^1/5)^x

=( $\sqrt[5]{243}$ )^x

= 3^x

Now that the left side is simplified, let's move to the right side

81^(x+5)=( $3^{4}$ )^(x+5) simplify 81 to base 3^4

= $x^{4(x+5)$ use the product of powers property to multiply the exponents together

= $x^{4x+20$

With both sides simplified, let's rewrite the equation, this time in simplified terms

$3^{x}$ = $3^{4x+20}$

x=4x+20 because both the bases are same, their exponential value must also be equal

-3x=20 solve the algebraic equation for x

x= $-\frac{20}{3}$

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baherus [9]

4π radians

<h3>Further explanation</h3>

We provide an angle of 720° that will be instantly converted to radians.

Recognize these:

From the conversion previous we can produce the formula as follows:

$\boxed{\boxed{ \ Radians = degrees \times \bigg( \frac{\pi }{180^0} \bigg) \ }}$
$\boxed{\boxed{ \ Degrees = radians \times \bigg( \frac{180^0}{\pi } \bigg) \ }}$

We can state the following:

Given α = 720°. Let us convert this degree to radians.

$\boxed{ \ \alpha = 720^0 \times \frac{\pi }{180^0} \ }$

720° and 180° crossed out. They can be divided by 180°.

$\boxed{ \ \alpha = 4 \times \pi \ }$

Hence, $\boxed{\boxed{ \ 720^0 = 4 \pi \ radians \ }}$

- - - - - - -

<u>Another example:</u>

Convert $\boxed{ \ \frac{4}{3} \pi \ radians \ }$ to degrees.

$\alpha = \frac{4}{3} \pi \ radians \rightarrow \alpha = \frac{4}{3} \pi \times \frac{180^0}{\pi }$

180° and 3 crossed out. Likewise with π.

Thus, $\boxed{\boxed{ \ \frac{4}{3} \pi \ radians = 240^0 \ }}$

<h3>Learn more </h3>

A triangle is rotated 90° about the origin brainly.com/question/2992432
The coordinates of the image of the point B after the triangle ABC is rotated 270° about the origin brainly.com/question/7437053
What is 270° converted to radians? brainly.com/question/3161884

Keywords: 720° converted to radians, degrees, quadrant, 4π, conversion, multiply by, pi, 180°, revolutions, the formula