Question 1187994

"can u pls. help me write the following exponential equations in logarithmic form?" 1.7^x=49 2.6^-3=(1/126) 3.12^2=144   also this...find the value of the following logarithmic expressions. 1.log3 243 2.log6 (1/216) 3.log0.25 16   thank u so much for the help.  
<pre>This is in no way as COMPLEX as that woman made it out to be.

{{{highlight_green(matrix(2,5, Exponential, "form:", 1.7^x, "=", 49, Logarithmic, "form:", log (1.7, (49)), "=", x))}}}
If you need a value, then just enter that into a calculator. 
If it's difficult to enter, then just enter the change-of-base version: {{{log ((49))/log ((17))}}}
You can now do nos. 2 & 3 the same way.


The value of the following logarithmic expression: {{{highlight_green(matrix(1,2, "1.", log (3, 243)))}}}
Enter the above into a calculator. 
Again, if it's difficult to do so, then just enter the change-of-base version: {{{log ((243))/log ((3))}}}
If you need to calculate without a calculator, then do the following:
 {{{matrix(1,3, x, "=", log (3, (243)))}}} ----- Setting {{{log (3, (243))}}} equal to x
{{{matrix(1,3, 3^x, "=", 243)}}} ----- Converting to EXPONENTIAL form
{{{matrix(1,3, 3^x, "=", 3^5)}}} ------ Converting 243 to base 3
 {{{highlight_green(matrix(1,5, x, "=", highlight(5), "=", highlight(log (3, (243)))))}}} ------ Bases are equal and so are their exponents</pre>