# Math

How do I solve e^(2x)+10e^(x)-75=0 and 3^(x+2)=7^(x-5)?

1. 👍 0
2. 👎 0
3. 👁 80
1. For e^(2x)+10e^(x)-75=0
Let
y=e^x
then
y² = e^(2x)
Substitute in above equation,
y²+10y-75=0
Factor and solve for y.
Note that the domain of y (=e^x) is (0,∞), so any negative root for the quadratic equation must be rejected.

For 3^(x+2)=7^(x-5)
take logarithm on both sides, and apply the exponent rule to get
(x+2)*ln 3 = (x-5)*ln 7
Solve for x. I get x=14 approx.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Calculus - derivatives of e

Find an equation of the tangent line to the graph of y = e^(−x^2) at the point (5, 1/(e^25)). My work: y' = -2xe^(-x^2) y' when x = 5 = -10e^25 y - (1/e^25) = -10e^25 * (x - 5) y = (-10e^25) (x - 5) + (1/e^25) This is incorrect.

asked by Anna on March 19, 2018
2. ### MATH PLZ SOMEONE HELP

7. Suppose you earn \$10 each hour you babysit. Which function describes the relationship between your total earnings E and the number of hours you babysit, h? (1 point) E(h) = 10h E(h) = h + 10 E(h) = h – 10 h = 10E

asked by HIHELP on April 7, 2015
3. ### How do I do this.?(Math.)

Use the Substitution method to solve the system of equations. y - 2x = -5 3y - x = 5 Solve one of the equations for x or y. Let's solve the first one for y: y - 2x = -5 y = 2x - 5 Now let's substitute 2x - 5 for y in the second

asked by Margie on February 5, 2007
4. ### Algebra

To solve the system of equations, which expression could be substituted for x into the first equation? 3x-5y=14 x+4y=10 a)10-4y b)4y+10 c)(1/4)x+(5/2) d)(-1/4)x+(5/2) I have another problem just like this one so if you could

5. ### Substitution Method-Plz help

Use the Substitution method to solve the system of equations. x + y = -4 x - y = 2 solve for x in the second equation. x= y+2 Put that in for x in the first equation: x+y=-4 (y+2) + y = -4 solve for y. Then, x= y+2 i don't get

asked by Svetlana on October 17, 2006
1. ### chemistry

CoSO4 + KI + KIO3 + H2O  Co(OH)2 + K2SO4 + I2 2KI yield I2 + 2e 2KIO2 10e yield I2 are there 10 electrons being transferred or just 5 only

asked by eng on June 6, 2010
2. ### Calculus

Let a thing rod of length a have a density distribution function p(x)+10e^(-.1x), where x is measured in cm and p in grams per centimeter. A) if the mass of the rod is 30 g, what is the value of a? B) For the 30g rod, will the

asked by Lauren on February 24, 2015
3. ### Algebra

There are 4 problems that I don't understand how to solve so, please help me. A numerical explanation with words explanation would be nice. Thank you tutors. Rewrite each equation so it is in the form ax + b = c or x + d/e = f,

asked by anon on December 9, 2015
4. ### Chemisdtry - Lewis Structures (check + help)

Draw Lewis structures for each of the following ion: CO3 (2-) I tried this method below, i do not know where am i going wrong, please help me understand this concept for ions. Valence Electrons 4e- + 18e- = 22e- Noble gas Config

asked by Farah on February 13, 2011
5. ### Math

If you write the function P=10e^−2t in the form P=P0a^t, then P0= a= .

asked by George Carl on March 19, 2018
6. ### chemistry

The heat of fusion of ice is 6.00 kJ/mol. Find the number of photons of wavelength = 6.42 x 10e-6 m that must be absorbed to melt 2.00 g of ice.

asked by mw on November 13, 2011