solve the exponential equation with base "a " algebraically. approximate the result to three decimal places. 8^(-2-x)=431

Question

solve the exponential equation with base "a " algebraically. approximate the result to three decimal places.

8^-2-x=431

Answer 1

log₈ 431 = log 431 / log 8

log 431 / log 8 = 2.634 / 0.903

2.634 / 0.903 = 2.917

2.917 = -2 - x

Can you solve for x and answer?

Answer 2

let y = -2-x

8^y = 431

8 squared = 64

8 cubed = 512

y is much closer to 3 than to 2

maybe 8^2.9 = about 431, then set 2.9 =-x-2 and solve for x

if a is the base then a=8

use a calculator

y = 2.9172

-x= 2.9172 +2 = 4.9172

x =-4.9172

for 3 decimal places

x=-4.917

or you could use a graphing calculator too