Write the equation in exponential form. log4 1/16 = -2

lyudmila [28]

Answer:

x=2, x=-5

Step-by-step explanation:

to work more comfortably, the first thing we need to do is work the equation linearly, for that we take advantage of the property of logarithms that tells me that $log(a^{b})=b*log(a)$

in this way, the equation remains as:

$log(12^{x^{2} +5x-4 } )=log(12^{5x+6} ) \\ (x^{2} +5x-4 )*log(12)=(5x+6) *log(12)\\x^{2} +5x-4 = 5x+6$

Now we clear the equation so that it is of the form $ax^{2} +bx+c=0$

$x^{2} +5x-2x=6+4\\ x^{2} +3x-10=0$

finally, we apply the equation to solve second degree equations

$x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}$

$x = \frac{-3 \pm \sqrt {3^2-4*1*(-10)}}{2*1}\\ x = \frac{-3 \pm \sqrt {9+40}}{2}\\ x = \frac{-3 \pm 7}{2}$

x=2 and x=-5

Done

5 0

4 years ago

In a two-digit number the units digit is three less than the tens digit. If the digits are reversed, the sum of the reversed num

makvit [3.9K]

Answer:

74.

Step-by-step explanation:

Let the number be xy.

Then from the given data

x = y + 3..........(1)

The numerical value of xy is 10x + y so the second equation is

10x + y + 10y + x = 121

11x + 11y = 121 Simplifying:

x + y = 11

x = -y + 11 .........(2) Adding equations (1) and (2):

2x = 14

x = 7

and therefore y = 7 - 3 = 4.

7 0

4 years ago

Read 2 more answers

Right triangles abc and dbc with right angle c are given below. If cos(a)=15,ab=12 and cd=2, find the length of bd.

dmitriy555 [2]

see the attached figure to better understand the problem

we have that

$cos(A)=\frac{1}{5} \\ AB=12\ units\\ CD=2\ units$

Step 1

Find the value of AC

we know that

in the right triangle ABC

$cos (A)=(AC/AB)\\AC=AB*cos(A)$

substitute the values in the formula

$AC=12*(1/5)\\ AC=2.4\ units$

Step 2

Find the value of BC

we know that

in the right triangle ABC

Applying the Pythagorean Theorem

$AB^{2} =AC^{2}+BC^{2}\\ BC^{2}=AB^{2} -AC^{2}$

substitute the values

$BC^{2}=12^{2} -2.4^{2}\\BC^{2}= 138.24\\ BC=11.76\ units$

Step 3

Find the value of BD

we know that

in the right triangle BCD

Applying the Pythagorean Theorem

$BD^{2} =DC^{2}+BC^{2}$

substitute the values

$BD^{2} =2^{2}+11.76^{2}$

$BD=11.93\ units$

therefore

the answer is

the length of BD is 11.93 units

8 0

3 years ago

Read 2 more answers

Write an equation

Valentin [98]

Y-1=4(x-(-2))
y-1=4x+8
Is this what you wanted ?

5 0

3 years ago

What is the first step in solving the quadratic equation x2 – 40 = 0?

Sonbull [250]

Answer:

x=20

Step-by-step explanation:

1-reoder the terms

2-Move constant to the right

3-dive both sides

just hit the image and you will get a representation on how to do it

8 0

1 year ago