Question

PLEASE HELP ME!!! SOLVE FOR X!!! THANKS!!!!! (look at pic)

Answer 1

`x=698.771`

Explanation:

`log_(2x) (5(3)/(2))=(1)/(3)`

`(5(3)/(2))*3=In(2x)*1`

`7.24247=In(2x)`

`e^(7.24247)=2x`

÷
`2` ÷
`2`

`698.771=x`

Answer 2

x = 698.771

Explanation:

`\sf \rightarrow \log _(2x)\left(5^{(3)/(2)}\right)=(1)/(3)`

apply ln rules

`\sf \rightarrow \frac{\ln \left(5^{(3)/(2)}\right)}{\ln \left(2x\right)}=(1)/(3)`

cross multiply

`\sf \rightarrow \ln \left(5^{(3)/(2)}\right)\cdot \:3=\ln \left(2x\right)\cdot \:1`

simplify using calculator

`\sf \rightarrow 7.24247 = ln(2x)`

shift sides

`\sf \rightarrow e^(7.24247 )= 2x`

divide both sides by 2

`\sf \rightarrow 698.771= x`