2 problems solving for x

[sportsaholic2397]

I am having a hard time with two log problems.

3Log(4x-1)=2.1

This one i can do the guess and check method, but i would like some help on a better way....my guess and check answer is: x=1.5

and the other one is Xlog(43)=7+e^1.9..

i just don't know where to begin someone please help me. greatly appreciated.

 

[galactus]

3Log(4x-1)=2.1

Divide by 3:

\(\displaystyle log(4x-1)=0.7\)

Since base 10 is implied, remember the log rules:

\(\displaystyle 4x-1=10^{0.7}\)

\(\displaystyle x=\frac{10^{0.7}+1}{4}\approx 1.51\)

and the other one is Xlog(43)=7+e^1.9..

There's not much to this besides dividing by log(43).

\(\displaystyle x=\frac{7+e^{1.9}}{log(43)}\approx 8.4\)