cherrypiedelicious

i think it means solve for x and show what x is in terms of ln2

the answer key says that it should be x=(16ln2+4)/(ln2+8) 

i just dont know how to get there

using the area of a triangle formula would give you the area

A= 1/2bh

A= 1/2 (4)(8)

=1/2 (32)

=16units squared

not sure if i should assume the base is 4, i just eyeballed it 

x⁸-y⁸ 

difference of cubes

(x²-y²)(x⁴+x²y²+y⁴) 

first polynomial can be factored further

(x+y)(x-y)    (x⁴+x²y²+y⁴)

next polynomial can be factored further

x⁴ + 2x²y²-x²y²+y⁴

x⁴+2x²y²+y⁴- x²y²

^{first three terms factorable by perfect square}

(x²+y²)² - x²y²

(x²+y²)² - (xy)²

difference of squares again

(x²+y²+xy)(x²+y²-xy)

first polynomials factored form and second polynomials factored form put together

(x+y)(x-y)(x²+y²+xy)(x²+y²-xy)

sorry if formatting is weird

9^5-x = 1/√15^4x

9^5-x = 1/15^4x(½)

9^5-x = 15^4x(½)(-1)

9^5-x = 15^-2x

9⁵・9^-x = 15^-2x

3²⁽⁵⁾・32^(-x) = 15^-2x

3^10-2x = 15^-2x

ln3^10-2x = ln15^-2x

(10-2x)ln3 = (-2x)ln15

10ln3- 2xln3 = -2xln15

10ln3 = -2xln15 + 2xln3

10ln3 = -2(xln15 + xln3)

(10ln3)/-2 = xln15 + xln3

-5ln3 = xln(15/3)

-5ln3 = xln5

(-5ln3)/ln5 = x