how to solve 5^8x=115

Question

i need to solve this equation and round answer to four decimal places

Answer 1

Changing the equation we have: Log₅ (5^8x) = log₅ 115=> 8x = Log₅115= (log 115/log5)=2.9482 => we solve for x = 2.9482/8 = 0.3685

Answer 2

5^8x = 115

 

To get the 8x out of the exponent, take the log base 5 of both sides:

 

log₅(5^8x) = log₅(115)

 

8x = log₅(115)

 

x = (1/8)log₅(115)

 

Use a calculator to calculate the answer.  If you can't do log₅ on your calculator, here's a natural log (ln) solution:

 

ln(5^8x) = ln(115)

 

(8x)ln(5) = ln(115)

 

x = ln(115)/8ln(5)