Question

What is the solution to the equation 4 2x ≈ 3 ?

Answer 1

sorry I mean for 2x to be as an exponent

Answer 2

4 ^2x ≈ 3

Answer 3

\[4^{2x}=3\]
\[2x=\frac{\ln(3)}{\ln(4)}\]
\[x=\frac{\ln(3)}{2\ln(4)}\] then a calculator

Answer 4

What exactly does ln represent

Answer 5

it means the natural logarithm. you cannot solve equations with the variable in the exponent without logs. what class is this for?

Answer 6

algebra 2!! I just don't understand the difference between LN and LOG The topics are logarithms and exponents and i dont understand any of it

Answer 7

I got .76 for the answer but i think its wrong

Answer 8

ok i will try to explain

Answer 9

thank you so much!!!

Answer 10

LOG means log base ten, whereas LN means log base e

Answer 11

those are the two you have on your calculator, and for this problem it makes no difference what you use

Answer 12

if i want to solve
\[b^x=A\] for x, say for example i want
\[2^x=50\] then i can solve in one step. i can write
\[x=\frac{\ln(50)}{\ln(2)}\] or i can write
\[x=\frac{\log(50)}{\log(2)}\] i will get the same answer in either case (you can try it with a calculator and see)

Answer 13

as for the topic of logs and exponents, you should understand that logs ARE exponents. and you should be able to go between logarithmic form and exponential form quickly. that will clear up a lot. so in general
\[b^x=y\iff \log_b(y)=x\] and switching should become routine
\[10^3=1000\iff \log_{10}(1000)=3\] for example or
\[2^5=32\iff \log_2(32)=5\]

Answer 14

but you only have two logarithms on your calculator, so what i used is sometimes called the "change of base" formula. for example i know how to solve
\[2^x=32\] which is the same as finding
\[\log_2(32)\] but the reason i know that is because i know
\[2^5=32\] so x = 5
and so
\[\log_2(32)=5\] but if i want
\[\log_2(50)\] i .e i want to solve
\[2^x=50\] i cannot do it because 50 is not an integer power of 2. that is why i would use the "change of base " formula and solve
\[2^x=50\] or
\[\log_2(50)\] by writing
\[x=\log_2(50)=\frac{\ln(50)}{\ln(2)}\]now i can use a calculator to get the number

Answer 15

Oh okay, thank you for all your help I really appreciate it. So wait was. 76 right for the first one? Because that's what I got when i plugged it on my calculator