The exponential equation and approximate the result, correct to 9 decimal places. a) 3(4x−1)=11 b) 6x+3=3x To solve for x.

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The exponential equation and approximate the result, correct to 9 decimal places.  a) 3(4x−1)=11  b) 6x+3=3x  To solve for x.

averes8 · Accepted Answer

Step 1  a) We have,  3(4x−1)=11  Applying log to the base 10 on both sides,  ⇒log10⁡3(4x−1)=log10⁡11  ⇒ (4x−3)log10⁡3=log10⁡11  ⇒4x−1=(log1011)/(log10⁡3)  ⇒4x−1=log3⁡11  ⇒ x=(1/4)[(log3⁡11)+1]  ⇒ x=0.795664585  (Rounded to 9 decimals)   Identities used :   (loga⁡x)/(loga⁡y)=logy⁡x  log⁡ ab=blog⁡ a  Step 2  b) We have,  6x+3=3x  Applying log to base 2 on both sides,  ⇒(x+3)log2⁡6=x(log2⁡3)  ⇒(x+3)log2⁡(3×2)=x(log2⁡3)  ⇒(x+3)[(log2⁡3)+(log2)]=x(log2⁡3)  ⇒(x+3)[(log2⁡3)+1]=x(log2⁡3)  ⇒ x(log2⁡3)+3(log2⁡3)+x+3=x(log2⁡3)  ⇒log2⁡33+x+3=0  ⇒log2⁡9+x+3=0  ⇒ x=−3−log2⁡9  ⇒ x=−6.169925001  (Rounded to 9 decimals)   Identities used :   loga⁡xy=(loga⁡x)+(loga⁡y)  log⁡ ab=blog⁡ a

The exponential equation and approximate the result, correct to 9 decimal places. a) 3^{(4x-1)}=11 b) 6^{x+3}=3^{x} To solve for x.

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