How do you use logarithms to solve for x in $5^(x+1)=24$ ?

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Answer 1 · 2018-07-12T15:28:43

$color(blue)(x~~0.974635869)$

$5^(x+1)=24$

Taking logarithms of both sides:

$ln(5^(x+1))=ln(24)$

Form the laws of logarithms:

$log(a^b)=blog(a)$

$(x+1)ln(5)=ln(24)$

Divide by $ln(5)$

$x+1=ln(24)/ln(5)$

$x=ln(24)/ln(5)-1~~0.974635869$

How do you use logarithms to solve for x in 5^(x+1)=245^(x+1)=24?