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anonymous
 one year ago
Please help. I don't want the answer just the steps to solve it myself thanks so much.
Solve for x and express your answer as a logarithm.
3(5^x) = 48
Simplify your answer as much as possible.
anonymous
 one year ago
Please help. I don't want the answer just the steps to solve it myself thanks so much. Solve for x and express your answer as a logarithm. 3(5^x) = 48 Simplify your answer as much as possible.

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marco26
 one year ago
Best ResponseYou've already chosen the best response.0just use \[a ^{x}=y\] >\[\log _{a}y=x\]

Owlcoffee
 one year ago
Best ResponseYou've already chosen the best response.1\[(3)(5^x)= 48\] When we want to solve an exponential equation, called like this because the variable right now is in the exponent, we have to use the reciprocate operation in order to bring the x down as a normal variable and not an exponent. What is reciprocate to exponents?, well Logarithms. In essence, we can use any logarithm we want, but we always take the logarithm with the convenient base in order to make things simple, so, we will can begin by getting rid of the 3 by dividing both sides by 3: \[5^x=\frac{ 48 }{ 3 }\] \[5^x=16\] So, now, what we will do is take the logarithm with base 5, which means: \(\log_{5} \) on both sides of the equation, further on, use the property of logarithms \(\log_{a} b^n=n \log_{a} b\) to bring the variable "x", down from the exponent: \[5^x=16\] \[\log_{5} 5^x=\log_{5} 16\] \(x \log_{5} 5=\log_{5} 16\) ...and \(\log_{5} 5=1\) so therefore: \[x=\log_{5} 16\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much for taking the time out of your day to help me it it means a lot.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0\[3(5^x) = 48\]Dividing both sides by 5, we would get \[5^x = \frac{48}{3} \qquad \implies 5^x = 16\] and now we can take the natural log of both sides to find x. \[\log_5 (5^x) = \log_5 (16) \]\[x = \log_5(16)\] Using the change of base formula we can simplify \(\log_5(16) \) into a fractional exponent. Remember that \(\log_a(x) = \dfrac{\log_b(x)}{\log_b(a)}\) Applying this you would get \[\color{red}{\boxed{x=\log_5(16) = \frac{\log(2^4)}{\log(5)}=\frac{4\log(2)}{\log(5)}}}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0dividing both sides by 3*
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