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February 10th, 2017, 07:29 AM   #1
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Logarithm function

Hi,

If*$\displaystyle log10(b)=1.8*and*loga(b)=2.5752$, what is*a? How does the change of base rule apply here when there are two unknowns a & B ?

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amphi
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February 10th, 2017, 07:54 AM   #2
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Quote:
Originally Posted by amphinomos View Post
Hi,

If*$\displaystyle log10(b)=1.8*and*loga(b)=2.5752$, what is*a? How does the change of base rule apply here when there are two unknowns a & B ?

Thanks,
amphi
$\log_a{b} = \dfrac{\log_{10}{b}}{\log_{10}{a}}$

$2.5752 = \dfrac{1.8}{\log_{10}{a}}$

$\log_{10}{a}= \dfrac{1.8}{2.5752}$

$a = 10^{\frac{1.8}{2.5752}}$
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February 27th, 2017, 01:14 PM   #3
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Math Focus: Algebra and Trigonometry
Loagarithms equate to Exponents

Really like Skeeter's solution, but when working with logarithms I get to exponents as soon as possible...

log b = 1.8
loga b = 2.5752

logb a = 1/2.5752

b^(1/2.5752) = a

10^(1.8 (1/2.5752)) = a

10^(1.8/2.5752) = a

Since logarithms equate to exponents.

Last edited by y2kevin; February 27th, 2017 at 01:23 PM. Reason: clearify math.
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