Simplify: log6^(36/6^-10)
I need all of the steps.
I need this ASAP because this assignment is due tomorrow.
Thanks
To simplify the expression log6^(36/6^-10), we'll work step by step using the rules of logarithms. Let's break it down:
Step 1: Recall the property of logarithms that states loga(b^c) = c * loga(b). This allows us to bring down the exponent as a coefficient:
log6^(36/6^-10) = (36/6^-10) * log6
Step 2: Simplify the fraction within the logarithm:
36/6^-10 = 36 * 6^10
= (6^2 * 6^10) (using the rule: (a^b)^c = a^(b * c))
= 6^12
= 2^12 * 3^12 (using the rule: 6 = 2 * 3)
Step 3: Rewrite the expression with the simplified fraction:
log6^(36/6^-10) = (2^12 * 3^12) * log6
Step 4: Use another rule of logarithms: loga(b * c) = loga(b) + loga(c). This allows us to split the logarithm into separate terms:
log6^(36/6^-10) = 2^12 * log6 + 3^12 * log6
Now, depending on the level of simplification required, you can leave it as is, or further evaluate the exponential values.
I hope this helps! Let me know if you have any further questions.