Question

Can anyone help solve this exponents/logarithm question

Answer 1

Answer:

x=0.355

Step-by-step explanation:

5^5x=4^3-2x

$5x=6log_{6}(2)-4log_{6}(2)x\\\\5x+4log_{6}(2)x=6log_{6}(2)\\\\(5+4log_{6}(2))x=6log_{6}(2)\\\\x=\frac{6log_{6}(2)}{5+4log_{6}(2)}\\\\x=\frac{6log_{6}(2)}{log_{6}(6^{5})+log_{6}(2^{4} )}\\\\x=\frac{6log_{6}(2)}{log_{6}(6^{5}*2^{4})}\\\\x=\frac{6log_{6}(2)}{log_{6}(16*6^{5})}\\\\x=6log_{16*6^{5}}(2)\\\\x=6log_{124416}(2)\\\\6log_{124416}(2)=0.354509$

3 decimal places of 0.354509 is 0.355