Question

how would i solve 19^(4x-15)=11?

Answer 1

19^(4x-15)=11

take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(19^(4x-15))=ln(11)

The lefthand side of the equation is equal to the exponent of the logarithm argument because the base of the logarithm equals the base of the argument.
4xln(19)-15ln(19)=ln(11)

Since -15ln(19) does not contain the variable to solve for, move it to the righthand side of the equation by adding 15ln(19) to both sides.
4xln(19)=15ln(19)+ln(11)

Divide each term in the equation by 4ln(19).
x=(15ln(19)+ln(11))/(4ln(19))
x=3.9536