Solve the following exponential equation. Round to the nearest thousandth place( 3 decimal places) 5^3x+7 =311

Answer 1

5^(3x+7) = 311

3x+7 = 3.566

3x = -3.434

x = -1.145

(5^3 = 125, 5^4=625, so you know 3x+7 is between 3 and 4, maybe about 3.5, 3.566 looks in the right neighborhood, ball park or close enough

Last comment: you wrote 5^3x+7. Technically that's (5^3x)+7 but you probably meant 5^(3x+7) If you did actually mean (5^3x)+7, then you have 5^3x = 311-7 = 304

and 3x=3.552, x=1.184)