Tuesday

October 21, 2014

October 21, 2014

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

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 11:05amUsually 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**

Math - Exponential equation - Solve the exponential equation. Express your ...

math - when solving the exponential equation, 2^2x-1=16 what do I do first? do I...

Chemisrt - What is pre-exponential factor for diffusion, because i have a ...

Math (Logarithms) - How do u do logarithms where there is a log on one side and ...

Precalculus - This is for solving exponential/logarithmic functions: (This is a ...

Precalc - Are exponential equations the same as exponential functions? I am ...

calculus - PLEASE help me. y=log(x+1) a. Write the equation as an exponential ...

Calculus - Given y=log(x), what is dy/dx? If you have to derive this from first ...

exponential equation-Algebra - Solve the exponential equation. Express the ...

Pre Calculus - solving exponential equations with exponents on each side 5^x =4...