Posted by **marcus** on Tuesday, November 20, 2012 at 10:48am.

Okay, I'm really fuzzy about my log and exponential chapter. For example, solving some exponential equation such as e^3x-7 x e^-2x=4e

I assume I start this equation by taking the natural log of both sides, but how will I know just by looking at an equation weather I need to find the log or the natural log?

Also, graphing. How to do you know where to put the base graph? Such as f(x)= log_1/2_x?

- Pre calculus -
**Steve**, Tuesday, November 20, 2012 at 11:05am
Usually you take logs to the base of the number having exponents. In your example, you have e^(3x-7), so take logs base e.

If you had written 2^(x+3) * 2^(x-7) = 32 then you'd take logs base 2.

As for graphing, just recall the all exponent/log graphs look the same, except for their slopes.

e^x looks just like 10^x. They both go through (0,1). e^x goes through (1,e) and 10^x goes through (1,10).

Fractional bases are just reflected through the y-axis, since (1/2)^x = 2^-x.

Now, logs look just like exponentials, but reflected through the origin, since if

y = e^x,

x = ln y

fractional bases are reflected through the x-axis.

So, as for log_1/2(x) It looks like log_2(x) but upside-down.

Visit wolframalpha.com and enter

log_4 x

or whatever base you want. It will also remind you that log_4(x) = lnx/ln4.

This also explains the reflection using fractional bases. log_1/2(x) = lnx/ln 1/2, and ln 1/2 is negative.

## Answer This Question

## Related Questions

- Precalculus - This is for solving exponential/logarithmic functions: (This is a ...
- algebra - logarithms Solve the following equations 3^x-2=6 Add 2 to both sides ...
- pre-calculus - What is the base of the function F(x) = b to the power of x if ...
- Math (Logarithms) - How do u do logarithms where there is a log on one side and ...
- Chemistry - How do you do the inverse of absolute temperature? My kelvin ...
- Math - h(x) = log (6x+5/7x-4) Find a formula for the inverse function h^-1(x) h...
- Math - Exponential equation - Solve the exponential equation. Express your ...
- math - solve for x without using a calculator 5^(x+1) = 25 i know that x would ...
- Logs. - Can you please help me with the following log. problems? thanxs! Solve ...
- math - when solving the exponential equation, 2^2x-1=16 what do I do first? do I...

More Related Questions