Would you use the change base formula for this equation? (solving logarithmic and exponential equations)

Question

anonymous · Answer

$$\log(5)x=3$$

amistre64 · Answer

you can if you want ... and in latex:  log_5  gets you to the base 5

amistre64 · Answer

$$log_5x=3$$

anonymous · Answer

so how would you solve it. I need help understanding

amistre64 · Answer

well, a log is just an exponent of its base.

so i would solve it by basing each side by 5

$$\large 5^{log_5x}=5^3$$
$$x=5^3$$

amistre64 · Answer

if we start with:  x = 5^3

we can log each side:  log(x) = log(5^3)

we can pull out the exponent:  log(x) = 3 log(5)

then divide off the log(5):  log(x)/log(5) = 3

and the left side is just change of base:  log_5 (x) = 3

this is a better way to see the solution if you want to change of base it

anonymous · Answer

Ohhh okay thank you

amistre64 · Answer

youre welcome