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2 years ago

13

How can exponential and logarithmic functions be combined?

1 answer:

OLEGan [10]2 years ago

4 0

It really depends on the question and what you want to solve. An exponential function can be written as y = x^2 and if you are solving for y then it will be log(base x) y = 2.

More Examples:
3x = 15
(log both sides with base of 3)
log(3)3x = log(3)15
since log(3)3 = 1 then,
(1)x = log(3)15
x = log 15 / log 3
= 2.465

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10 POINTS<br> Find the surface area of the regular pyramid. Round to the nearest tenth if necessary.

NNADVOKAT [17]

Answer:

$SA=234.8\ yd^2$

Step-by-step explanation:

we know that

The surface area of the regular pyramid is equal to the area of the triangular base plus the area of its three triangular lateral faces

step 1

Find the area of the triangular base

we know that

The triangular base is an equilateral triangle

so

The area applying the law of sines is equal to

$A=\frac{1}{2}(14^2)sin(60^o)$

$A=\frac{1}{2}(196)\frac{\sqrt{3}}{2}$

$A=49\sqrt{3}=84.87\ yd^2$

step 2

Find the area of its three triangular lateral faces

$A=3[\frac{1}{2}bh]$

we have

$b=14\ yd$

Find the height of triangles

Applying the Pythagorean Theorem

$10^2=(14/2)^2+h^2$

solve for h

$100=49+h^2$

$h^2=100-49$

$h=\sqrt{51}\ yd$

substitute

$A=3[\frac{1}{2}(14)\sqrt{51}]$

$A=149.97\ yd^2$

step 3

Find the surface area

Adds the areas

$SA=84.87+149.97=234.84\ yd^2$

Round to the nearest tenth

$SA=234.8\ yd^2$

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Step-by-step explanation:

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