10log3
4
log1 + log2 + log3 = log(1*2*3) = log6
log325 + log34 = log3(25*4) = log3(100) = log10100/log103 = 2/log103
log4+log3=log(4x3)=log12
log3 [ 9 sqrt(3) ]= log3 [ 9 ] + log3 [ sqrt(3) ]= log3 [ 32 ] + log3 [ 31/2 ]= 2 + 1/2= 2.5
10log3
There is not a solution. Knowing how logarithms work helps. On the right hand side you have: log3(2*x) + log3(0.5).Adding logs is equivalent to multiplying (inside the log). This becomes: log3(0.5 * 2*x) = log3(x).Subtract log3(x) from both sides: log3(7x) - log3(x) = 0.Subtracting logs is equivalent to division (inside the log): log3(7x/x) = 0.So log3(7) = 0, which is Not true. No Solution.
They can be.
log3(x) + log9(x^3)=0 for any t >0 logt(x) = ln(x)/ln(t) so log9(x) = ln(x) / ln (9) = ln (x) / ( 2 * ln 3) = log3(x) /2 or log3(x) = 2 log9(x) log9(x^n) = n * log9(x) So log3(x) + log9(x^3) = log3(x) + 6 log3(x) = 7 log3(x) 7 log3(x) = 0 => log3(x) = 0 => x = 1
4
log1 + log2 + log3 = log(1*2*3) = log6
log33+log3x +2=3 log33+log3x=1 log3(3x)=1 3x=3 x=1 Other interpretation: log33+log3(x+2)=3 log3(3(x+2))=3 3(x+2)=27 x+2=9 x=7
1
log3 81 × log2 8 × log4 2 = log3 (33) × log2 (23) × log4 (40.5) = 3 × (log3 3) × 3 × (log2 2) × 0.5 × (log4 4) = 3 × 1 × 3 × 1 × 0.5 × 1 = 9 × 0.5 = 4.5
An expresssion
Find 102a if log2=a and log3=b B has no purpose in this question If a=log2, then 102a =102(log2)