How do you simplify e^3lnx^5+4lny^2?

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Answer 1 · 2018-04-12T12:54:20

$x^{6} + 8 ln (y)$ $x^6+8ln(y)$

By the laws of logarithms:

$a^{{log}_{a} (b)} = b$ $a^(log_a(b))=b$

${log}_{a} (b^{c}) = c {log}_{a} (b)$ $log_a(b^c)=clog_a(b)$

$e^{3 ln (x^{2}) + 4 ln (y^{2})}$ $e^(3ln(x^2)+4ln(y^2)$

Rewriting:

${(e^{ln (x^{2})})}^{3} + 8 ln (y)$ $(e^(ln(x^2)))^3+8ln(y)$

${(x^{2})}^{3} + 8 ln (y)$ $(x^2)^3+8ln(y)$

$x^{6} + 8 ln (y)$ $x^6+8ln(y)$