Question

Solve this 14^(x+3)=21

Answer 1

are there options?

Answer 2

No

Answer 3

I really need help )=

Answer 4

ok lets see

Answer 5

\[\Large 14^{(x+3)}=21\]We can start by taking the natural log of both sides,\[\Large \ln\left[14^{(x+3)}\right]=\ln 21\]

From here we can apply a rule of logarithms,\[\Large \color{royalblue}{\log(a^b) \qquad=\qquad b\cdot \log(a)}\]

Answer 6

\[\Large (x+3)\ln\left[14\right]=\ln21\]Understand that part so far? :o

Answer 7

little bit

Answer 8

To finish solving for x, we would continue by dividing both sides by ln14.\[\Large (x+3)=\frac{\ln21}{\ln14}\]There is nothing being applied to the brackets around x+3 so we can drop the brackets now.\[\Large x+3=\frac{\ln21}{\ln14}\]Then subtract 3 from each side.\[\Large x=\frac{\ln21}{\ln14}-3\]

Then use a calculator to get your final answer! :D