Express $(100^3)^5$ with a base of $10$. I don't get this.
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1They are asking you to express the given quantity as $10^b$, for suitable $b$. – André Nicolas Jun 08 '16 at 00:05
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So I replace 100 as 10? – Anonymous Jun 08 '16 at 00:06
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As a start to finding $b$, note that $100=10^2$, so we are looking at $((10^2)^3)^5$. Now find $b$ using laws of exponentiation. – André Nicolas Jun 08 '16 at 00:08
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That would equal (100)^3)^5=(100000)^5 ... big number – Anonymous Jun 08 '16 at 00:11
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First let's combine the exponents by using the rule $(x^a)^b = x^{a\cdot b}.$ Thus we have $$(100^3)^5 = 100^{3 \cdot 5} = 100^{15}.$$ Next, we note that $100 = 10^2$. So we replace $100$ in the above equation with $10^2$ and apply the same rule.$$100^{15} = (10^2)^{15} = 10^{2\cdot 15} = 10^{30}.$$ Thus, we've expressed it with base 10. Let me know if you have any other questions!
David
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Can anybody please provide a step by step solution to the following expression ?
(a 2 ) 5 (2x 2 ) 4 2 5 (a 3 ) 3 (x 3 ) 2
– Anonymous Jun 08 '16 at 00:12 -
Never mind. Just look at this link: http://math.stackexchange.com/questions/1817725/simplify-the-expression-a252x24-over25a33x32# I'm still stuck on it. – Anonymous Jun 08 '16 at 00:13
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Go ahead and post them, if this is satisfactory for this particular question please mark it as an accepted solution! – David Jun 08 '16 at 00:13
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Up votes are appreciated too! They allow users to offer bounties on their questions and get them answered quicker. I'm checking out your other question now! – David Jun 08 '16 at 00:20
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It means going for this representation $$ (100^3)^5 = 10^x \quad (*) $$ The left hand side is $$ (100^3)^5 =100^{15} = (10^2)^{15} = 10^{30} $$ Or we take the logarithm of both sides of $(*)$: $$ \ln((100^3)^5) = \ln(10^x) \iff \\ 5 \ln(100^3) = 15 \ln(100) = x \ln(10) \iff \\ x = 15 \ln(100)/\ln(10) = 30 \ln(10)/\ln(10) = 30 $$
mvw
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