Solve for x if 5^x=200

Mathematics

2 answers:

Sphinxa [80]3 years ago

7 0

Answer:

ln200/ln5

Step-by-step explanation:

ln5^x=ln200

xln5=ln200

x=ln200/ln5

vampirchik [111]3 years ago

5 0

Answer:

x ≈ 3.29

Step-by-step explanation:

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form:

x = $\frac{ln(200)}{ln(5)}$

Decimal Form:

x = 3.29202967 … ≈ 3.29 (Round to what the question asks, in this case, I rounded to 2 decimal places)

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The radii of two circles are in the ratio of 3 to 1. Find the area of the smaller circle if the area of the larger circle is 27

Naddik [55]

ANSWER
$3\pi sq.\: in.$

EXPLANATION

Let R be the radius of the bigger circle and r, be the radius of the smaller circle.

Then their ratio is given as,

$R:r=3:1$

We can rewrite it as fractions to get,

$\frac{R}{r} = \frac{3}{1}$

We make R the subject to get,

$R = 3r$

The area of the bigger circle can be found using the formula,

$Area=\pi {r}^{2}$

This implies that,

$Area=\pi ({3r})^{2}$

$Area=9\pi {r}^{2}$

But it was given in the question that, the area of the bigger circle is 27π.

$27\pi=9\pi {r}^{2}$

We divide through by 9π to get,

$3 = {r}^{2}$

This means that,
$r = \sqrt{3}$

The area of the smaller circle is therefore

$= \pi {( \sqrt{3}) }^{2}$

$= 3\pi$