How do you solve $10^(4x-1) = 5000$ ?

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Answer 1 · 2018-03-02T19:00:45

$x=ln(5000)/(1ln(4))+1/4$

Apply the natural logarithm to both sides:

$ln(10^(4x-1))=ln(5000)$

$ln(10^(4x-1))=(4x-1)ln(10),$ as the exponent property for logarithms tells us that $ln(x^y)=yln(x)$ .

$ln(10^(4x-1))=ln(5000)hArr(4x-1)ln(10)=ln(5000)$

Solve for $x:$

$((4x-1)cancelln(10))/cancelln(10)=ln(5000)/ln(10)$

$4xcancel(-1+1)=ln(5000)/ln(10)+1$

$(cancel(4)x)/cancel4=ln(5000)/(4ln10)+1/4$

How do you solve 10^(4x-1) = 500010^(4x-1) = 5000?