2.13A · Exponential and Logarithmic Equations and Inequalities

Try each one on paper first, then tap to check.

1. 1.

   Solve (exact answer + rounded to 3 decimals): $\log_5 x=2$
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2. 2.

   Solve (exact answer + rounded to 3 decimals): $e^{-x}=3.65$
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3. 3.

   Solve (exact answer + rounded to 3 decimals): $\log x+\log(x-3)=1$
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4. 4.

   Solve (exact answer + rounded to 3 decimals): $80e^{0.045x}=240$
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5. 5.

   Solve (exact answer + rounded to 3 decimals): $\log_3(5-2x)=\log_3(3x+1)$
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6. 6.

   Solve (exact answer + rounded to 3 decimals): $3-\log_4(x+3)=5$
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7. 7.

   Solve (exact answer + rounded to 3 decimals): $\ln 12=\ln(2x+3)-\ln(x-4)$
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8. 8.

   Solve (exact answer + rounded to 3 decimals): $e^{2x-1}+68=207$
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9. 9.

   Solve (exact answer + rounded to 3 decimals): $\log_2(3x-52)-4=\log_2 x$
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10. 10.

    Solve (exact answer + rounded to 3 decimals): $\log_3\sqrt{2x+3}=1$
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11. 11.

    Solve (exact answer + rounded to 3 decimals): $\ln x+\ln(x-10)=\ln 24$
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12. 12.

    Solve (exact answer + rounded to 3 decimals): $3\left(2^{x+4}\right)-12=-10$
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13. 13.

    Solve with a graphing calculator (3 decimals): $0.5e^{x/4}=12$
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14. 14.

    Solve with a graphing calculator (3 decimals): $\frac34\ln\left(\frac45x\right)+10=12$
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15. 15.

    Use $A=Pe^{rt}$. Mr. Kelly currently has $450,000 in an investment account. He originally put in $200,000 into the account which earns 4.5% interest. How many years has he been investing in this account?
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