How do you solve $10^(5x+2)=5^(4-x)$ ?

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Answer 1 · 2016-07-10T00:46:24

$x = (4ln(5)-2ln(10))/(5ln(10)+ln(5))~~0.1397$

Using the property that $ln(a^x)=xln(a)$ :

$10^(5x+2) = 5^(4-x)$

$=> ln(10^(5x+2)) = ln(5^(4-x))$

$=>(5x+2)ln(10) = (4-x)ln(5)$

$=>5ln(10)x+2ln(10) = 4ln(5)-ln(5)x$

$=>5ln(10)x+ln(5)x = 4ln(5)-2ln(10)$

$=>(5ln(10)+ln(5))x = 4ln(5)-2ln(10)$

$=>x = (4ln(5)-2ln(10))/(5ln(10)+ln(5))~~0.1397$

How do you solve 10^(5x+2)=5^(4-x)10^(5x+2)=5^(4-x)?