1003138501
Level:
A
Solve.
\[ \log_2(3x-5)=4\]
\( x=7 \)
\( x=3 \)
\( x=\frac{11}3 \)
\( x=-\frac13 \)
Logarithmic equations and inequalities
1003138502
Level:
A
Solve.
\[ \log_{\frac13}\!(3-x)=0\]
\( x=2 \)
The equation has no solution.
\( x =3 \)
\( x=-4 \)
1003138503
Level:
A
How many solutions in the set of integers does the following equation have?
\[ \log_{\frac12}\!(x+6)=\log_{\frac12}\!(3x-6) \]
exactly one positive solution
exactly one negative solution
exactly one solution equal to zero
no solutions
1003138504
Level:
A
Solve.
\[ \log_3(-5x-2)=\log_3(x-4) \]
The equation has no solution.
\( x=\frac13 \)
\( x=3 \)
\( x=\frac32 \)
1003138505
Level:
A
Solve.
\[ \ln(-2x-6)=\ln(-3x-9) \]
The equation has no solution.
\( x=-3 \)
\( x=3 \)
\( x=-15 \)
1003138506
Level:
A
Solve.
\[ \frac{\log_3x-3}{3+\log_3x}=0\]
\( x=27 \)
\( x=9 \)
\( x_1=\frac1{27};\ x_2=27 \)
infinitely many solutions
1003138507
Level:
A
Solve.
\[ \log_4x=2-\log_48\]
\( x=2 \)
\( x=1 \)
\( x=0 \)
The equation has no solution.
1003138508
Level:
A
How many solutions does the following equation have?
\[ 2\log x^4-\log x^5-3\log x^3= 12 \]
exactly one positive solution
exactly one negative solution
exactly one integer solution
no solutions
1003138509
Level:
A
Solve.
\[ \log_2(x-1)+\log_2x=1 \]
\( x=2 \)
\( x_1=-1;\ x_2=2 \)
\( x_1=-2;\ x_2=1 \)
\( x=1 \)
1003138510
Level:
A
How many solutions does the following equation have?
\[ \log(x-2)+\log(x+2)=2\log(2-x) \]
no solutions
exactly one solution
exactly two solutions
infinitely many solutions