MHB Rewrite in exponential form: Log(6) 1294 = 4

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The discussion focuses on rewriting logarithmic equations in exponential form. The equation Log(6) 1294 = 4 is confirmed, with a suggestion that it might be Log(6) 1296 instead. The relationship between logarithms and exponents is emphasized, specifically that log_b(a) = c implies b^c = a. Additionally, participants evaluate Log(4) 64, noting that 4^3 equals 64, and Log(16) 4, recognizing that 16 raised to the power of 1/2 equals 4. The conversation highlights the fundamental properties of logarithms and their exponential counterparts.
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Rewrite in exponential form:
Log(6) 1294 = 4
Log(w) v = t

Ln(1/4) = x
Evaluate

Log(4) 64 = ?

Log(16) 4 = ?
 
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Vi Nguyen said:
Rewrite in exponential form:
Log(6) 1294 = 4

sure that isn't 1296 ?Log(w) v = t

if you meant w to be the base of the logarithm ... $w^t = v$

Ln(1/4) = x

$e^x = \dfrac{1}{4}$
Evaluate

Log(4) 64 = ?

note that $4^3 = 64$

Log(16) 4 = ?

note $16^{1/2} = 4$

logarithm to exponential relationship ...

$\log_b(a) = c \implies b^c = a$
 
Thanks
 
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