Question 1187994
<br>
I suspect the way you posted the problems misled the other tutors.  Very probably the first set of three problems are these:<br>
(1) {{{7^x=49}}}<br>
(2) {{{6^(-3)=1/216}}}  <-- that one includes a typo -- you showed 1/126....<br>
(3) {{{12^2=144}}}<br>
To convert each of those to logarithmic form, all you need to remember is this:<br>
THE LOGARITHM IS THE EXPONENT<br>
(1) The exponent is x; obviously the base is 7 --> "log (base 7) of 49 is x" --> {{{log(7,(49))=x}}}<br>
(2) The exponent is -3; the base is 6 --> "log (base 6) of 1/216 is -3" --> {{{log(6,(1/216))=-3}}}<br>
(3) The exponent is 2; the base is 12 --> "log (base 12) of 144 is 2" --> {{{log(12,(144))=2}}}<br>
For the other problems you again only need to remember the same thing.<br>
(1) {{{log(3,(243))=x}}} --> "log (base 3) of 243 is x" --> THE LOGARITHM (x) IS THE EXPONENT --> {{{3^x=243}}}<br>
(2) {{{log(6,(1/216))=x}}} --> "log (base 6) of 1/216 is x"  --> THE LOGARITHM (x) IS THE EXPONENT --> {{{6^x=1/216}}}<br>
(3) {{{log(0.25,(16))=x}}} --> "log base 0.25 of 16 is x"  --> THE LOGARITHM (x) IS THE EXPONENT --> {{{0.25^x=16}}}<br>
I leave it to you to find the values of x for those last three problems.<br>