Given exponential equations,a) 3^{(4x - }=11b) 6^{x + 3}=3^{x}To solve for x

EunoR 2020-11-17 Answered

Given exponential equations,
a) 3(4x 1)=11
b) 6x + 3=3x
To solve for x

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Expert Answer

lamusesamuset
Answered 2020-11-18 Author has 93 answers

Sub part a)
We have,
3(ax  1)=11
Applying log to the base 10 on both sides,
 log10 3(4x  1)= log1011
 (4x  1)log103=log1011
 4x  1 =(log1011)/(log103)
 4x  1 = log311
 x=(1/4)[(log311) + 1]
 x=0.795664585
(Rounded to 9 decimals)
Identities used:
(logax)/(logay)=logyx
log ab=b log a
Sub part b)
We have,
6x + 3=3x
Applying log to base 2 on both sides,
 (x + 3)log2 6=x(log23)
 (x + 3)log2 (3× 2)=x(log23)
 (x + 3)[(log23) + (log22)]=x(log23)
 (x + 3)[(log23) + 1]=x(log23)
 x(log23) + 3(log23) + x + 3=x(log23)
 log233 + x + 3=0
 log29 + x + 3=0
 x= 3  log29
 x= 6.169925001
(Rounded to 9 decimals)
Identities used:
logaxy=(logax) + (logay)
logab=b log a

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