Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\mathsf{log_2\:(x + 2) = 5}[/tex]

[tex]\mathsf{x + 2 = 2^5}[/tex]

[tex]\mathsf{x + 2 = 32}[/tex]

[tex]\boxed{\boxed{\mathsf{x = 30}}}[/tex]

[tex]\mathsf{4\:log_3\:(x - 40) = 16}[/tex]

[tex]\mathsf{log_3\:(x - 40) = 4}[/tex]

[tex]\mathsf{x - 40 = 3^4}[/tex]

[tex]\mathsf{x - 40 = 81}[/tex]

[tex]\boxed{\boxed{\mathsf{x = 121}}}[/tex]

[tex]\mathsf{12 - \:log_7\:(x - 1) = 10}[/tex]

[tex]\mathsf{log_7\:(x - 1) = 2}[/tex]

[tex]\mathsf{x - 1 = 7^2}[/tex]

[tex]\mathsf{x - 1 = 49}[/tex]

[tex]\boxed{\boxed{\mathsf{x = 50}}}[/tex]

[tex]\mathsf{2\:log_4\:(x - 2) + 1 = 7}[/tex]

[tex]\mathsf{2\:log_4\:(x - 2) = 6}[/tex]

[tex]\mathsf{log_4\:(x - 2) = 3}[/tex]

[tex]\mathsf{x - 2 = 4^3}[/tex]

[tex]\mathsf{x - 2 = 64}[/tex]

[tex]\boxed{\boxed{\mathsf{x = 66}}}[/tex]

[tex]\Large\boxed{\begin{array}{l}\rm a)~\sf \log_2(x+2)=5\\\sf x+2)=2^5\\\sf x+2=32\\\sf x=32-2\\\sf x=30\\\rm b)~\sf 4\log_3(x-40)=16\\\sf \log_3(x-40)=\dfrac{16}{4}\\\\\sf \log_3(x-40)=4\\\sf x-40=3^4\\\sf x-40=81\\\sf x=40+81\\\sf x=121\end{array}}[/tex]

[tex]\Large\boxed{\begin{array}{l}\rm c)~\sf12-\log_7(x-1)=10\\\sf \log_7(x-1)=12-10\\\sf \log_7(x-1)=2\\\sf x-1=7^2\\\sf x-1=49\\\sf x=49+1\\\sf x=50\end{array}}[/tex]

[tex]\Large\boxed{\begin{array}{l}\rm d)~\sf2\log_4(x-2)+1=7\\\sf 2\log_4(x-2)=7-1\\\sf 2\log_4(x-2)=6\\\sf \log_4(x-2)=\dfrac{6}{2}\\\\\sf \log_4(x-2)=3\\\sf x-2=4^3\\\sf x-2=64\\\sf x=64+2\\\sf x=66\end{array}}[/tex]