Question

Can anyone help solve this exponents/logarithm question

Answer 1

x=0.355

Explanation:

5^5x=4^3-2x

`5x=6log_(6)(2)-4log_(6)(2)x\\\\5x+4log_(6)(2)x=6log_(6)(2)\\\\(5+4log_(6)(2))x=6log_(6)(2)\\\\x=(6log_(6)(2))/(5+4log_(6)(2))\\\\x=(6log_(6)(2))/(log_(6)(6^(5))+log_(6)(2^(4) ))\\\\x=(6log_(6)(2))/(log_(6)(6^(5)*2^(4)))\\\\x=(6log_(6)(2))/(log_(6)(16*6^(5)))\\\\x=6log_(16*6^(5))(2)\\\\x=6log_(124416)(2)\\\\6log_(124416)(2)=0.354509\\\\`

3 decimal places of 0.354509 is 0.355