Solve for x. 7^x=e^(x+5)

Question

zehanz · Answer

If you take the ln on both sides, you can use the rule: $$\ln a^b = b \cdot \ln a$$so:$$\ln 7^x=\ln e^{x+5}$$By the rule, this is equal to$$x \cdot \ln7 = (x+5) \ln e$$

Of course, you know that ln e = 1, so you can solve for x now...

anonymous · Answer

as the matter of fact, I was able to come up with that but im confused when it comes x. so, the answer should be x=5/In(7)?

zehanz · Answer

xln7=x+5, so xln7 - x = 5.
Factor out x: x(ln7 - 1)=5.
Divide by ln7 -1:$$x=\frac{ 5 }{ \ln7 -1 }$$

anonymous · Answer

wow, that makes sence! thank you so much! :)

anonymous · Answer

May I ask another question? im stuck with this math question.  5=55(1.3)^x. for x using logs to slove the equation.