All categories

2 years ago

Logb(x-1) + logb(x+2) = logb(8-2x)

Mathematics

1 answer:

Aleksandr [31]2 years ago

7 0

Answer:

x=2

Step-by-step explanation:

log_x(y)+log_x(z)=log_x(yz), so logb(x-1) + logb(x+2)=logb((x-1)(x+2)). next subtract logb(8-2x) from both sides to get logb((x-1)(x+2))-logb(8-2x)=0. log_x(y) - log_x(z) = log_x(y/z). so now we have logb((x-1)(x+2)/(8-2x)). now you can put it into exponential form: (x-1)(x+2)/(8-2x)=b^0=1 now just solve for x:

(x-1)(x+2)= 8-2x, x^2 + x -2 = 8-2x, x^2 + 3x -10 = 0, (x+5)(x-2)=0 x=-5, x=2. plug both into the original equation to check which one is correct, since log_x(y) can't have a negative y, x=-5 doesnt work

You might be interested in

Need help pls!!!! Algebra

PtichkaEL [24]

Answer:

Step-by-step explanation:

6 0

2 years ago

Find the area of the shaded regions below. Give your answer as a completely

timama [110]

Area is 74 in/cm/mm^2 hope this helps :)

8 0

2 years ago

PLEASE HURRY I NEED HELP ON MY EXAM! 15PTS!

Wittaler [7]

Answer:

I III and IV

Step-by-step explanation:

It cant be All four since yeah but im really sure that what i put is the answer

3 0

2 years ago

I need help with this

evablogger [386]

Answer:

A) (-8, -16)

B) (0, 48)

C) (-4, 0), (-12, 0)

Step-by-step explanation:

A) the vertex is the minimum y value.

extremes of a function we get by using the first derivation and solving it for y' = 0.

y = x² + 16x + 48

y' = 2x + 16 = 0

2x = -16

x = -8

so, the vertex is at x=-8.

the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16

B) is totally simple. it is f(0) or x=0. so, y is 48.

C) is the solution of the equation for y = 0.

the solution for such a quadratic equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case here

a=1

b=16

c=48

x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =

= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)

x1 = -8 + 4 = -4

x2 = -8 - 4 = -12

so the x- intercepts are (-4, 0), (-12, 0)

6 0

2 years ago

If cos x= sin(20 + x)° and 0° < x < 90°, what is the value of x

ZanzabumX [31]

If cos x= sin(20 + x)° and 0° < x < 90° then value of x is 35 degrees

<em><u>Solution:</u></em>

Given that:

$cos x= sin (20 + x)$

We know that,

$sin (a+b)=sin a \times cos b+cos a \times sin b$

$cos x= sin (20 + x) = sin 20 cos x + cos 20 sin x$

$cos x-sin20 \times cos x=cos 20 \times sin x$

Taking cos x as common,

$cos x(1-sin 20)=cos 20 \times sin x$

$\frac{(1-sin 20)}{(cos 20)}=\frac{sin x}{cos x }\\\\tan x = \frac{(1-sin 20)}{(cos 20)}$

By trignometric functions,

sin 20 = 0.34202

cos 20 = 0.939692

So,

$tan x = \frac{1 - 0.34202}{0.939692}\\\\tan x = 0.7002$

Therefore,

x = arc tan (0.7002)

x = 35 degrees

Therefore value of x is 35 degrees

<h3><u>Method 2:</u></h3>

cos x = sin (20 + x)

sin and cos are co - functions, which means that:

cos x = cos [90 - (20 + x)]

cos x = cos (90 - 20 - x)

cos x = cos (70 - x)

Therefore, x = 70 - x

x + x = 70

2x = 70

x = 35

Therefore value of x is 35 degrees

3 0

3 years ago