All Answers 358524 Answers

Take logs of both sides.Always the same technique. 

If 5^n =3125

then log(5^n) = log 3125

n log 5 = log 3125

n= (log 3125)/log5. 

log 3125 = 3.495 approx  and     log 5 = 0.7 approx

so answer in this case is

n=3.495/0.7 = 4.99 approx. ( I  rounded off the numbers,you will see that if you

raise 5 to the power 4.99 you actually get 3075)

There is a quicker way to do this. Since log( a/b ) = log a  - log b

then  log(4x) - log (2x-3) can be written as

log (4x)/(2x-3)

So log(4x)/(2x-3) =log 6

then

(4x)/(2x-3) =6    by equivalence

4x = 12x-18

8x=18

x=18/8=9/4

I should have written:    solve(y-ln(x),x) above. (I.e. entered a minus sign, not an equals sign)

.

You can also type in something like:   solve(y=ln(x),x) and press equals to get:

The calculator here will solve some algebraic equations, and will give information about integral so and derivatives.  For example, if you enter:  x^2-3 and then press the equals sign, you get the following:

max.Dave

​

What was wrong with my answer Max ?

Do you need to be spoon fed the answer?  Is this so you can just copy it as your own work?

I gave you a good outline.  If you needed the dots joined for you you could have just asked.

I am always prepared to give a great deal of my time to students who are actually trying to learn!

Thanks for the point recognition Michael :)

As below:

.

Use the calculator on the home page here:

Examples:

Round 5.4 to the nearest integer:   5

Round 5.7 to the nearest integer:   6

Round 5.674 to two decimal places:  5.67

etc.

Interesting.  It calculates for ages, then gives up the ghost!!

Mathcad also fails to find a solution when presented with the same two equations.

If you replace the first r^n by 243r, both Mathcad and Wolfram Alpha find the solution immediately.

As the two before me have said, your answer of -4 is correct :)

that is     

2--(-6)¹

=2+(-6)¹

=2-6

= -4

Where did you see the answer +4, was it on a calculator?

3-2x3+2(4-7)

= 3-6+2(-3)

= 3-6+-6

= 3-6-6

= -3 - 6

= -9

3-6+2(-3)= -9 

3-(6+-3) = 0 

Find the function value. Round to four decimal places.

tan 53°54​'

tan(53+54/60) = 1.371342293302

Solve for X 
log 4x - log (2x-3) = log 6

\(log( 4x) - log (2x-3) = log 6\\ log(2* 2x) - log (2x-3) = log 6\\ log(2)+log(2x) - log (2x-3) = log3+log2\\ log(2x) - log (2x-3) = log(3)\\ log(\frac{2x}{2x-3})=log3\\ \frac{2x}{2x-3}=3\\ 2x=6x-9\\ -4x=-9\\ x=2\frac{1}{4}\)

Thanks asinus, it is always nice to see you here :)

Hi Irondome,

Her is your graph.

1.83 x 11.99 =$21.94 cost of 1.83 meters.

$21.94 x 1.05=$23.04 Total cost plus 5% sales tax.

Find the function value. Round to four decimal places.

tan 53°54​'

coefficient in front of x³ = 3 - 4 = -1.

coefficient in front of x = 7 - 12 = -5.

How did I get that?

First, ask, how many ways you get the form of ax³ if you pick 2 terms and multiply?

First way,3 times x³

Second way, -4x times x²

No other ways.

So the coefficient of x³ = 3 + (-4) = 3 - 4 = -1

You do the coefficient of x one as above too.

\(\sqrt{\dfrac{1}{96}}\times \sqrt3\\ =\sqrt{\dfrac{3}{96}}\\ =\sqrt{\dfrac{1}{32}}\\ =\dfrac{\sqrt{1}}{\sqrt{32}}\\ =\dfrac{1}{4\sqrt{2}}\\ =\dfrac{1\times\sqrt2}{4\sqrt2 \times \sqrt2}\\ =\dfrac{\sqrt2}{8}\)

\(f(x)= 3x-2x^2\)

\(f'(x)=\displaystyle\lim_{h\rightarrow 0}\dfrac{f(x+h)-f(x)}{h}\\ \;\;\;\;\;\;\;\;= \displaystyle\lim_{h\rightarrow 0}\dfrac{(3(x+h)-2(x+h)^2)-(3x-2x^2)}{h}\\ \;\;\;\;\;\;\;\;=\displaystyle\lim_{h\rightarrow 0} \dfrac{3x+3h-2x ^2-4xh-2h^2-3x+2x^2}{h}\\ \;\;\;\;\;\;\;\;=\displaystyle\lim_{h\rightarrow 0}\dfrac{3h-4xh-2h^2}h\\ \;\;\;\;\;\;\;\;=\displaystyle\lim_{h\rightarrow 0} (3-4x-2h)\\ \;\;\;\;\;\;\;\;= 3-4x\)

-(-6)¹= -(-6)=+6

2/3 approximately.

6666666666666667/10000000000000000 exactly.

How does -(-6)1 = 6?, Because -(-6)=+6 x 1=6

Full eqaution. 

2--(-6)1 = 2 + (-6) x 1

             =2 - 6

             =-4