a) [latex]log_4(log_3x)=0[/latex] [latex]log_3x=4^0[/latex] [latex]log_3x=1[/latex] [latex]x=3^1[/latex] [latex]x=3[/latex] [latex]L=log_4(log_33)=log_41=0[/latex] [latex]P=0[/latex] [latex]L=P[/latex] c) [latex]log_5left[3+log_4left(log_2x+10 ight) ight]=1[/latex] [latex]3+log_4left(log_2x+10 ight)=5^1[/latex] [latex]3+log_4left(log_2x+10 ight)=5[/latex] [latex]log_4left(log_2x+10 ight)=5-3[/latex] [latex]log_4left(log_2x+10 ight)=2[/latex] [latex]log_2x+10=4^2[/latex] [latex]log_2x+10=16[/latex] [latex]log_2x=16-10[/latex] [latex]log_2x=6[/latex] [latex]x=2^6[/latex] [latex]x=64[/latex] [latex]L=log_5left[3+log_4left(log_264+10 ight) ight]=log_5left[3+log_4left(log_22^6+10 ight) ight]=[/latex] [latex]log_5left[3+log_4left(6log_22+10 ight) ight]=log_5left[3+log_4left(6cdot 1+10 ight) ight]=[/latex] [latex]log_5left[3+log_4left(6+10 ight) ight]=log_5left[3+log_416 ight]=[/latex] [latex]log_5left[3+log_44^2 ight]=log_5left[3+2log_44 ight]=[/latex] [latex]log_5left[3+2cdot 1 ight]=log_5left[3+2 ight]=log_55=1[/latex] [latex]P=1[/latex] [latex]L=P[/latex]
