All Answers 358406 Answers

400+552=952

952/2=476

Proof

476*2=952

x^2 - 64    =

(x + 8) (x - 8)

do 1/2*pi*4.7*47

It should look like that.

4.21x + 5.39 = 12.07(2.01 - 4.72x)     multipy through by 100 to help clear some decimals

421x + 539  = 1207 (2.01 - 4.72x)        simplify the right side

421x + 539  = 2426.07 - 5697.04x    add 5697.04 to both sides, subtract 539 from both sides

6118.04 x =  1887.07        divide both sides by 6118.04

x = 1887.07 / 6118.04  

23 is a PRIME number!. It is not a multiple of any number.

RESULT: UNDEFINED!!.

Thanks Heureka, ElecricPavlov and guest      

Solve for x over the real numbers:
(4 x-5)^(2 x+5) = 1

Take the natural logarithm of both sides:
log(4 x-5) (2 x+5) = 0

Split log(4 x-5) (2 x+5) into separate parts with additional assumptions.
Assume 4 x-5!=0 from log(4 x-5):
2 x+5 = 0 for 4 x-5!=0
 or log(4 x-5) = 0

Subtract 5 from both sides:
2 x = -5 for 4 x-5!=0
 or log(4 x-5) = 0

Divide both sides by 2:
x = -5/2 or log(4 x-5) = 0

Cancel logarithms by taking exp of both sides:
x = -5/2 or 4 x-5 = 1

Add 5 to both sides:
x = -5/2 or 4 x = 6

Divide both sides by 4:
Answer: |x = -5/2                 or                         x = 3/2

If you mean "how much interest would this loan cost you", then this is what you have to do:

1) You have to calculate a monthly payment for the loan, which comes to:$287.12

2)Then you multiply $287.12 x 9 months =$2,584.08

3)Then you subtract $2,584.08 -$2,500 =$84.08 interest - cost of the loan.

...just to add...To get the 10^9 If you count the number of digits after the leftmost first digit that will indicate what ^(to the power of) will be...I don't recall mathematics teacher or science teacher explaining this but picked this tip up whilst trying to learn how to read and understand equations too

1/2

dass a fraction mang

1/2

dass a fraction mang

How to graph f(x)=-3x^2+10

Good point Heureka....guess we can all save a lot of computations by realizing either

1  The base must = 1     so 4x-5 =1      x= 6/4 = 3/2

or

2  The exponent must = 0    so 2x+5=0   x = - 5/2

Simple !

Find all values of x for which (4x-5) to the power of 2x+5=1.

\(\begin{array}{|rclcrcll|} \hline && (4x-5)^{(2x+5)} &=& 1 && \qquad & | \qquad \ln() \\ && \ln( (4x-5)^{(2x+5)} ) &=& \ln(1) && \qquad & | \qquad \ln(1) = 0 \\ && \ln( (4x-5)^{(2x+5)} ) &=& 0 && \qquad & | \qquad \ln(a^b) = b\cdot \ln(a) \\ && (2x+5) \cdot \ln( 4x-5 ) &=& 0 \\ (2x+5) &=& 0 & or &\qquad \ln( 4x-5 ) &=& 0 \\ 2x &=& -5 & or &\qquad e^{\ln( 4x-5 )} &=& e^{0} \\ \mathbf{ x } & \mathbf{=} & \mathbf{-\frac52} & or &\qquad 4x-5 &=& 1 \\ && & &\qquad 4x &=& 6 \\ && & &\qquad x &=& \frac64 \\ && & &\qquad \mathbf{ x } & \mathbf{=} & \mathbf{\frac32} \\ \hline \end{array}\)

So the exponent must be zero => 2x+5 = 0 => x = -5/2

or the base must be 1 => 4x-5 = 1 => x = 3/2

Find all values of x for which (4x-5) to the power of 2x+5=1.

\(\begin{array}{|rclcrcll|} \hline && (4x-5)^{(2x+5)} &=& 1 && \qquad & | \qquad \ln() \\ && \ln( (4x-5)^{(2x+5)} ) &=& \ln(1) && \qquad & | \qquad \ln(1) = 0 \\ && \ln( (4x-5)^{(2x+5)} ) &=& 0 && \qquad & | \qquad \ln(a^b) = b\cdot \ln(a) \\ && (2x+5) \cdot \ln( 4x-5 ) &=& 0 \\ (2x+5) &=& 0 & or &\qquad \ln( 4x-5 ) &=& 0 \\ 2x &=& -5 & or &\qquad e^{\ln( 4x-5 )} &=& e^{0} \\ \mathbf{ x } & \mathbf{=} & \mathbf{-\frac52} & or &\qquad 4x-5 &=& 1 \\ && & &\qquad 4x &=& 6 \\ && & &\qquad x &=& \frac64 \\ && & &\qquad \mathbf{ x } & \mathbf{=} & \mathbf{\frac32} \\ \hline \end{array}\)

To raise something to a 'POWER' and get   ' 1 '   the exponent must be  '0'

so  2x+5   MUST = 0     2x+5 = 0   means x= -5/2

For every (6+1) flowers she has to spend $48

49/(6+1)  x 48 = 7 x 48 = $336

ln(1/904)/(ln(1)-ln(4))

\(\begin{array}{|rcll|} \hline && \frac{ \ln( \frac{1}{904} ) } { \ln(1)-\ln(4) } \qquad & | \qquad \ln(\frac{a}{b}) = \ln(a) - \ln(b) \\\\ &=& \frac{ \ln(1)-\ln(904) } { \ln(1)-\ln(4) } \qquad & | \qquad \ln(1) = 0\\\\ &=& \frac{ 0-\ln(904) } { 0-\ln(4) } \\\\ &=& \frac{ -\ln(904) } { -\ln(4) } \\\\ &=& \frac{ \ln(904) } { \ln(4) } \\\\ &=& \frac{ 6.80682936039 } { 1.38629436112 } \\\\ &=& 4.91008948121 \\ \hline \end{array}\)

5 = 3^m

Take log of both sides to get

log(5)= m log(3)

m= log(5)/log(3) = 1.46497