(a) If $$ 5^{x}=48 $$, then $$ x=\square $$ (b) If $$ 18^{-x}=5 $$, then $$ x=\square $$

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UpStudy AI · Accepted Answer

**(a)**  
Given  
$$
5^{x} = 48
$$  
Take the natural logarithm of both sides:  
$$
\ln(5^{x}) = \ln(48)
$$  
Use the logarithm power rule:  
$$
x \ln(5) = \ln(48)
$$  
Now solve for $$ x $$:  
$$
x = \frac{\ln(48)}{\ln(5)}
$$

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**(b)**  
Given  
$$
18^{-x} = 5
$$  
Take the natural logarithm of both sides:  
$$
\ln(18^{-x}) = \ln(5)
$$  
Use the logarithm power rule:  
$$
-x \ln(18) = \ln(5)
$$  
Now solve for $$ x $$:  
$$
x = -\frac{\ln(5)}{\ln(18)}
$$
**(a)** $$ x = \frac{\ln(48)}{\ln(5)} $$ **(b)** $$ x = -\frac{\ln(5)}{\ln(18)} $$

(a) If \( 5^{x}=48 \), then \( x=\square \) (b) If \( 18^{-x}=5 \), then \( x=\square \)

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