How do I solve this Exponential and Logarithmic Function?
1.Find the value of http://www.mathway.com/math_image.as...MB03?p=30?p=22 when http://www.mathway.com/math_image.as...MB03?p=34?p=22 = 4.
My attempt: http://www.mathway.com/math_image.as...MB03?p=30?p=22=http://www.mathway.com/math_image.as...MB03?p=34?p=22= 4
http://www.mathway.com/math_image.as...MB03?p=58?p=22=4
27x=1
x= 1/27.
When checked on a calculator it doesn't work. I don't understand what to do. Is there a way to solve this without using calculators?
2. Solve the equation http://www.mathway.com/math_image.as...013?p=138?p=22
I don't have an attempt since I can't understand what operation to use.
Whoops, wrong category. Can I request for a Moderator (if there is one in here) to relocate this to Algebra?
Now how do I mark this thread as [SOLVED]? There was a prefix box when I was just making this thread earlier.
Re: How do I solve this Exponential and Logarithmic Function?(Sorry, wrong category)
Quote:
Originally Posted by
RPSGCC733 
^{3x} \\ &= 27^{3x} \\ &= \left( 27^x \right)^3 \\ &= 4^3 \\ &= 64 \end{align*})
Re: How do I solve this Exponential and Logarithmic Function?(Sorry, wrong category)
Quote:
Originally Posted by
RPSGCC733
Is the second question trying to solve for 
when } = 3 \end{align*})
?
Re: How do I solve this Exponential and Logarithmic Function?
Note that
^x = (3^{3\cdot 3})^x = 3^{3\cdot 3 \cdot x} = \ldots = ?)
)=3)
where =8)
thus you have to solve
=3 \Leftrightarrow x^3 = 8 \Leftrightarrow \ldots )
Re: How do I solve this Exponential and Logarithmic Function?(Sorry, wrong category)
Quote:
Originally Posted by
Prove It
Ah. Thanks! Didn't think that 3^{9x} was 3^3 raised to the third power all along.
Yeah, it was trying to solve for x.
Re: How do I solve this Exponential and Logarithmic Function?
1.) A similar approach to the one already posted:
)
)
}=64)
Re: How do I solve this Exponential and Logarithmic Function?
Quote:
Originally Posted by
Siron Note that
where
thus you have to solve
Many thanks.
Isn't multiplication in Logarithm denoted with a + sign? That part confused me.
Nevermind, I just realized it wasn't multiplication. was a logarithm of =8)
Re: Exponential and Logarithmic Function?(Sorry, wrong category)
Hello, RPSGCC733!
![\begin{array}{ccc}\text{Given:} & \log_x\left[\log_2(256)\right] \:=\:3 \\ \\ \text{Then:} & x^3 \:=\:\log_2(256) \\ \\ & x^3 \:=\:\log_2(2^8) \\ \\ & x^3 \:=\:8 \\ \\ & x \:=\:2 \end{array}](http://latex.codecogs.com/png.latex?\begin{array}{ccc}\text{Given:} & \log_x\left[\log_2(256)\right] \:=\:3 \\ \\ \text{Then:} & x^3 \:=\:\log_2(256) \\ \\ & x^3 \:=\:\log_2(2^8) \\ \\ & x^3 \:=\:8 \\ \\ & x \:=\:2 \end{array})
