Pre-Calc Log problems!?
Hi. I'm having trouble solving these two log equations:
Solve for x : NOTE: The number next to the log is the base!
log4(2x+3)=log4(15)
and
log2(x)=(1/3)log2(27)
A short explanation would be great! Thanks
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log₄(2x + 3) = log₄(15)
2x + 3 = 15
2x = 12
x = 6
:::::
log₂(x) = (⅓)log₂(27)
log₂(x) = log₂(27^⅓)
log₂(x) = log₂(∛27)
x = ∛27 = 3
2^(3-x)=5^(2x+a million) Take the organic logarithm of the two sides of the equation to eliminate the variable from the exponent. ln(2^(3-x))=ln(5^(2x+a million)) The left-hand fringe of the equation is comparable to the exponent of the logarithm argument because of the fact the backside of the logarithm equals the backside of the argument. -xln(2)+3ln(2)=ln(5^(2x+a million)) The exponent of a element interior a logarithm could be accelerated to the front of the expression utilising the 0.33 regulation of logarithms. The 0.33 regulation of logarithms states that the logarithm of a skill of x is comparable to the exponent of that skill cases the logarithm of x (e.g. log^b(x^(n))=nlog^b(x)). -xln(2)+3ln(2)=((2x+a million)ln(5)) eliminate the parentheses around the expression 2xln(5)+ln(5). -xln(2)+3ln(2)=(2xln(5)+ln(5)) on account that 2xln(5) consists of the variable to sparkling up for, pass it to the left-hand fringe of the equation via subtracting 2xln(5) from the two sides. -xln(2)+3ln(2)-2xln(5)=ln(5) element out the GCF of -x from each and every term in the polynomial. -x(ln(2))-x(2ln(5))=-3ln(2)+ln(5) element out the GCF of -x from -xln(2)-2xln(5). -x(ln(2)+2ln(5))=-3ln(2)+ln(5) Divide each and every term in the equation via (ln(2)+2ln(5)). -(x(ln(2)+2ln(5)))/(ln(2)+2ln(5))=-(3l... Simplify the left-hand fringe of the equation via canceling the straightforward words. -x=-(3ln(2))/(ln(2)+2ln(5))+(ln(5))/(l... Simplify the stunning-hand fringe of the equation via simplifying each and every term. -x=(-3ln(2)+ln(5))/(ln(2)+2ln(5)) Multiply each and every term in the equation via -a million. -x*-a million=(-3ln(2)+ln(5))/(ln(2)+2ln(5))*-... Multiply -x via -a million to get x. x=(-3ln(2)+ln(5))/(ln(2)+2ln(5))*-a million Simplify the stunning-hand fringe of the equation via simplifying each and every term. x=(3ln(2)-ln(5))/(ln(2)+2ln(5)) or x is approximately 0.12