How do you solve for #7^ { x ^ { 2} - 7x + 46} = 49^ { 3x + 5}#?

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Answer 1 · 2017-11-06T05:13:32

#x=4# or #9#

#7^(x^2-7x+46)=49^(3x+5)# can be written as

#7^(x^2-7x+46)=(7^2)^(3x+5)#

or #7^(x^2-7x+46)=7^(2xx(3x+5))#

or #7^(x^2-7x+46)=7^(6x+10)#

Hence #x^2-7x+46=6x+10#

i..e. #x^2-7x-6x+46-10=0#

or #x^2-13x+36=0#

or #x^2-9x-4x+36=0#

or #x(x-9)-4(x-9)=0#

i.e. #x-4=0# or #x-9=0#

i.e. #x=4# or #9#