How do you solve $ln (x^{7}) - ln (x^{2}) = 5$ $ln(x^7) − ln(x^2) = 5$ ?

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Answer 1 · 2018-05-22T00:55:50

Use properties of logarithms to combine the two natural logs and then pull the exponent out front.

$ln (x^{7}) - ln (x^{2}) = 5$ $ln(x^7)-ln(x^2)=5$

$ln (\frac{x^{7}}{x^{2}}) = 5$ $ln(x^7/x^2)=5$

$ln (x^{5}) = 5$ $ln(x^5)=5$

$5 ln (x) = 5$ $5ln(x)=5$

$ln (x) = 1$ $ln(x)=1$

$x = e$ $x=e$

How do you solve ln(x^7) − ln(x^2) = 5ln(x7)−ln(x2)=5ln(x^7) − ln(x^2) = 5?