Question

logx(5x+14)=2 solve for x

Answer 1

\[log_{10}(x(5x+14))=2\]?

Answer 2

@chris95????

Answer 3

\[10^{log_{10}(5x^2+14x)}=10^2=100\\5x^2+14x-100=0\\5(x^2+\frac{14}{5}x)=100\\5(x+\frac{14}{10})^2=100+5(\frac{14}{10})^2\\(x+\frac{14}{10})^2=20+\frac{196}{100}=\frac{549}{25}\\x=\pm \sqrt{\frac{549}{25}}-\frac{14}{10}\\x=\pm\frac{3\sqrt{61}}{5}-\frac{7}{5}\\\]

Answer 4

you need to make sure both solutions work.

Answer 5

logx(5x+14)=2 solve for x

I think you can easily solve it if you tranform it into exponential function.
Like this:
logx(5x+14)=2 == x^2 = 5x+14

equate the exponential func to zero:
x^2 = 5x+14
x^2 - 5x - 14 = 0
Through factoring:
(x-7) (x+5) = 0
Therefore,
x = -5, 7
Knowing that the answer should be positive, hence x = 7