How do i solve 5^x=3^(x+6)

I need help in trying to solve this question. Any and all help is greatly appreciated. Thankyou

Hi:

5^x=3^(x+6) - original equation

log(5^x) = log(3^(x+6) ) - take the logarithm of both sides of the equation to remove the exponents

xlog(5) = (x+6)log (3) - the power rule of logarithms

xlog(5) * 1/ log(5) = (x+6)log(3) * 1/log(5) - Multiplying the multiplicative inverse of a number ( log(5)) to both sides of the equation to move it to the other side of it

x = (x+6)log(3) /log(5) - multiplication


x* 1/(x+6) = (x+6)log(3) /log(5) * 1/(x+6) - Multiplying the multiplicative inverse of a number ( log(5)) to both sides of the equation to move it to the other side of it


x/(x+6) = log(3) /log(5) - multiplication

x/ x+6 = 0.477121254720/ 0.698970004336 - sloving the logs of 3 and 5

0.477121254720(x+6) = 0.698970004336x - cross multiplication


0.477121254720x+ 2.862727528318 = 0.698970004336x - multiplication


- 0.477121254720x+ 0.477121254720x+ 2.862727528318 = 0.698970004336x + - 0.477121254720x - Adding the additive inverse of a coefficient to both sides of the equation to move it to the other side of it

2.862727528318 = 0.221848749616x - Addition

2.862727528318 * 1 / 0.221848749616 = 0.221848749616x *1/0.221848749616 - Multiplying the reciprocal of a coefficient to both sides of the equation to solve for x

2.862727528318 /.221848749616 = x - Multiplication


12.903960618523 = x - Division


Proof or check

5^x=3^(x+6) - original equation

5^12.903960618523 = 3^(12.903960618523 +6) - plugging x with 12.903960618523

5^12.903960618523 = 3^(18.903960618523 )- Addition of 12.903960618523 and 6

1045878919.347605677546 = 1045878919.347605677546 - solving 5 to the power of 12.903960618523 and 3 to the power of 18.903960618523

it checks and equals