Value of x which satisfies the following relation (6/5) a log a x ⋅ log 10 a ⋅ log a 5=3 log 10 (x/10)+9 log 100 x+ log 4 2. This value of x lies between

Question

Value of x which satisfies the following relation (6/5) a log a x ⋅ log 10 a ⋅ log a 5=3 log 10 (x/10)+9 log 100 x+ log 4 2. This value of x lies between (A) (10,20) (B) (30,40) (C) (75,85) (D) (95,105)

Tardigrade Admin · Accepted Answer

(6/5) x log 10 5=3 log 10 x-1+3 log 10 x+1 (6/5) 5 log 10 x=(3 log 10 x/3)+3 ⋅ 3 log 10 x (6/5) ⋅ 5t=(3t/3)+3 ⋅ 3t 2 ⋅ 3 ⋅ 5t-1=3t ⋅((10/3)) 5t-2=3t-2 ((5/3))t-2=((5/3))0 t=2 log 10 x=2 x=100

Q. Value of $x$ which satisfies the following relation $\frac{6}{5} a^{l o g_{a} x \cdot l o g_{10} a \cdot l o g_{a} 5} = 3^{l o g_{10} \frac{x}{10}} + 9^{l o g_{100} x + l o g_{4} 2}$ . This value of $x$ lies between

$(10, 20)$

$(30, 40)$

$(75, 85)$

$(95, 105)$

Q. Value of x which satisfies the following relation 56​aloga​x⋅log10​a⋅loga​5=3log10​10x​+9log100​x+log4​2. This value of x lies between

(10,20)

(30,40)

(75,85)

(95,105)

56​xlog10​5=3log10​x−1+3log10​x+1 56​5log10​x=33log10​x​+3⋅3log10​x 56​⋅5t=33t​+3⋅3t 2⋅3⋅5t−1=3t⋅(310​) 5t−2=3t−2 (35​)t−2=(35​)0 t=2 log10​x=2 x=100

Q. Value of $x$ which satisfies the following relation $\frac{6}{5} a^{l o g_{a} x \cdot l o g_{10} a \cdot l o g_{a} 5} = 3^{l o g_{10} \frac{x}{10}} + 9^{l o g_{100} x + l o g_{4} 2}$ . This value of $x$ lies between

$(10, 20)$

$(30, 40)$

$(75, 85)$

$(95, 105)$