How do you solve -1 + 8e^(2x-5) = e

if anyone can break it down step by step I would appreciate it thanks

8 e^(2 x-5)-1 = e
Add 1 to both sides:
8 e^(2 x-5) = 1+e
Divide both sides by 8:
e^(2 x-5) = (1+e)/8
Take the natural logarithm of both sides:
2 x-5 = ln((1+e)/8)
Add 5 to both sides:
2 x = 5+ln((1+e)/8)
Divide both sides by 2:
x = 1/2 (5+ln((1+e)/8))

Hi:

-1 + 8e^(2x-5) = e - original equation

1+ -1 + 8e^(2x-5) = e + 1 - Adding 1 to both sides of the equation to remove the -1

8e^(2x-5) = e+1 - Addition

1/8* e^(2x-5) = (e+1)* 1/8 - Multiplying 1/8 to both side of the equation to remove the 8 from 8e^(2x-5)

e^(2x-5) = (e+1)/ 8 - Multiplication

ln(e^(2x-5) ) = ln((e+1)/ 8 ) - taking the logs of both side of the equation to remove the expontential

since e = 2.718281828459 - the value of e or the base of natural logarithm

2x-5 = ln(( 2.718281828459 + 1) /8) - Solving the logarithm of one side and replacing e with 2.718281828459

2x- 5 = ln( 3.718281828459/ 8) - Addition

2x -5 = ln ( 0.464785228557) - Division

2x - 5 = - 0.766179854162 - Solving the natural logarithm of the other side of the equation

2x- 5 + 5 = - 0.766179854162 + 5 - Adding 5 to both sides of the equation to remove the - 5

2x = 4.233820145838 - Addition

1/2 * 2x = 4.233820145838 * 1/2 - Multiplying 1/2 to both sides of the equation to solve for x

x = 4.233820145838 / 2 - Multiplication

x = 2.116910072919 - Division

Proof or check :

-1 + 8e^(2x-5) = e - original equation

-1 + 8*2.718281828459 ^(2x-5) = 2.718281828459 - replacing e with 2.718281828459


-1 + 8*2.718281828459 ^(2*2.116910072919 -5) = 2.718281828459 - replacing x with 2.116910072919


-1 + 8*2.718281828459 ^( 4.233820145838 - 5 ) = 2.718281828459 - Multiplication of 2 and 2.116910072919